{
  "solved_problems": [
    {
      "problem": {
        "dynamics": "dx1/dt = -2.5*x1 + x2*x3 + u0, dx2/dt = -2.5*x2 + x1*x3 + u1, dx3/dt = 5 - x1*x2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 0.25",
      "controllers": "u0 = -x2*x3 - 4*x1, u1 = -x1*x3 - 4*x2, u2 = -5 + x1*x2 - 5*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.8*x1 - 0.15*x2 + 0.2*x1**2 + u1, dx3/dt = -0.1*x3 + 0.1*x1 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.4,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 1.0",
      "controllers": "u0=-0.5*x1 - 0.2*x2, u1=-0.5*x2, u2=-0.5*x3 - 0.1*x1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.95*sin(x1) - 0.02*x2 + 0.01*x3 + u1, dx3/dt = -0.1*x3 + 0.02*x1 + u2, dx4/dt = -0.03*x4 + 0.01*x2 + u3",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 4.0",
      "controllers": "u0 = -3*x1 - 1.5*x2, u1 = -3*x2 + 0.8*sin(x1), u2 = -3*x3 - 0.05*x1, u3 = -3*x4 - 0.02*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 0.02*x1 - 0.1*x2 + u0, dx2/dt = 0.3*x1 - 0.05*x2 - 0.01*x1*x2 + u1, dx3/dt = 0.1*x2 - 0.02*x3 + u2",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [8.0, 12.0],
            [2.0, 4.0],
            [1.0, 3.0]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [20, 25],
            [15, 20],
            [10, 15]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "(x1 - 10)**2 + (x2 - 3)**2 + (x3 - 2)**2 - 50",
      "controllers": "u0=-0.52*x1 + 0.1*x2 + 5, u1=-0.3*x1 - 0.45*x2 + 0.01*x1*x2 + 1.5, u2=-0.1*x2 - 0.48*x3 + 1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 10*(x2 - x1) + u0, dx2/dt = 28*x1 - x2 - x1*x3 + u1, dx3/dt = x1*x2 - 8/3*x3 + u2, dx4/dt = -x2*x3 + 2.7*x4 + u3",
        "initial_set": {
          "type": "ball",
          "radius": 0.1,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 25.0,
          "center": [0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 400",
      "controllers": "u0=-60*x1 - 20*x2 - 2*x3, u1=-50*x1 - 35*x2 - 2*x4, u2=-2*x1 - 5*x2 - 12*x3, u3=-x1 - 2*x2 - 25*x4",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.1*x1 + 0.17*x2 + u0, dx2/dt = 0.1*x1 - 0.17*x2 + 0.4*x3 + u1, dx3/dt = -0.013*x3 + 0.0001*x1 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 3.5",
      "controllers": "u0=-0.8*x1 - 0.6*x2, u1=-0.6*x1 - 0.9*x2 - 0.7*x3, u2=-0.8*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.1*x2 - x1**3 + x1 + 0.3*cos(x3) + u1, dx3/dt = 1.2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 4.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 1",
      "controllers": "u0=-2*x1 - 0.5*x2, u1=-2*x2 + 0.1*x2 + x1**3 - x1 - 0.3*cos(x3), u2=-2*x3 - 1.2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 35*(x2 - x1) + x2*x3 + u0, dx2/dt = 55*x1 - x1*x3 - 13*x2 + u1, dx3/dt = x1*x2 - 3*x3 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.1,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 12.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 121",
      "controllers": "u0=-50*x1 - 40*x2 - 2*x2*x3, u1=-40*x1 - 30*x2 - 2*x1*x3, u2=-15*x3 - 2*x1*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -2*x1 + 6.7*x2 - x2*x3 + u0, dx2/dt = x1 + u1, dx3/dt = -x3 + x2**2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 5.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 9",
      "controllers": "u0=-8*x1 - 4*x2, u1=-4*x1 - 6*x2, u2=-4*x3 - 2*x2**2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 7*(x2 - x1 - 0.5*(x1**3 - x1)) + u0, dx2/dt = x1 - x2 + x3 + u1, dx3/dt = -14*x2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.1,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 4.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 9",
      "controllers": "u0=-10*x1 - 7*(x2 - x1 - 0.5*(x1**3 - x1)), u1=-5*x1 - 8*x2 - 2*x3, u2=14*x2 - 6*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.2*x1 + 0.3*x2*sin(x1) + u0, dx2/dt = -0.3*x2 + 0.2*x1*cos(x2) - 0.1*x1**2*x2 + u1",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 6",
      "controllers": "u0=-0.5*x1 - 0.3*x2*sin(x1), u1=-0.5*x2 - 0.2*x1*cos(x2) + 0.1*x1**2*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.3*x1 - 0.2*(1 + cos(x1))*x2 - 0.1*x1**3 + u1",
        "initial_set": {
          "type": "ball",
          "radius": 0.6,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [2, 2],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 2.0",
      "controllers": "u0=-0.5*x1 - x2, u1=-0.4*x1 - 0.6*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + 0.2*sin(x2) + u0, dx2/dt = -2*x1 - 0.5*x2 + u1",
        "initial_set": {
          "type": "box",
          "bounds": [
            [0.3, 0.7],
            [0.3, 0.7]
          ]
        },
        "unsafe_set": {
          "type": "union",
          "sets": [
            {
              "type": "box",
              "bounds": [
                [2.0, 3.0],
                [2.0, 3.0]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [-3.0, -2.0],
                [-3.0, -2.0]
              ]
            }
          ]
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 1",
      "controllers": "u0 = -x1 - 0.2*sin(x2), u1 = -x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2, dx2/dt = -0.2*x1 - 0.2*x2",
        "initial_set": {
          "type": "ball",
          "radius": 0.8,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 4.0,
          "center": [0, 0],
          "complement": true
        }
      },
      "barrier": "0.2*x1**2 + 0.2*x1*x2 + x2**2 - 2.8",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.1*x1 + 0.05*x2, dx2/dt = -0.05*x1 - 0.1*x2, dx3/dt = -0.2*x3",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 1",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.2*x1, dx2/dt = -0.3*x2",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 - 5",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.1*x1 - x2, dx2/dt = x1 - 0.1*x2",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.0,
          "center": [0, 0],
          "complement": true
        }
      },
      "barrier": "1*x1**2 + 1*x2**2 - 3.9",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1, dx2/dt = -0.4*x2, dx3/dt = -0.3*x3, dx4/dt = -0.6*x4",
        "initial_set": {
          "type": "ball",
          "radius": 0.8,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "2*x1**2 + 2.5*x2**2 + 3.33*x3**2 + 1.67*x4**2 - 7",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.4*x1 + 0.1*x2, dx2/dt = -0.5*x2 + 0.08*x3, dx3/dt = -0.6*x3 + 0.05*x1, dx4/dt = -0.3*x4",
        "initial_set": {
          "type": "ball",
          "radius": 0.7,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 4",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -x1 + x2*x3, dx2/dt = -x2 + x1*x3, dx3/dt = -x3 - x1*x2",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 0.25",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -x1, dx2/dt = -2*x2",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 - 2",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -x1 + 0.3*sin(x2) + u0, dx2/dt = -0.5*x2 + 0.2*x1 + u1, dx3/dt = -0.8*x3 + 0.1*sin(x1) + u2",
        "initial_set": {
          "type": "box",
          "bounds": [
            [0.8, 1.2],
            [0.6, 1.0],
            [0.4, 0.8]
          ]
        },
        "unsafe_set": {
          "type": "union",
          "sets": [
            {
              "type": "box",
              "bounds": [
                [3.5, 4.5],
                [3.0, 4.0],
                [2.5, 3.5]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [-4.5, -3.5],
                [-4.0, -3.0],
                [-3.5, -2.5]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [0.0, 0.5],
                [3.5, 4.0],
                [0.0, 0.5]
              ]
            }
          ]
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 12",
      "controllers": "u0 = -2*x1 - 0.3*sin(x2), u1 = -1.5*x2 - 0.2*x1, u2 = -2*x3 - 0.1*sin(x1)",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 - x1**3, dx2/dt = -0.5*x1 - 0.3*x2",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0],
          "complement": true
        }
      },
      "barrier": "0.8*x1**2 + 1.5*x2**2 - 4.0",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -x1, dx2/dt = -x2, dx3/dt = -0.9*x3, dx4/dt = -1.1*x4",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 1.5,
          "center": [0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "0.5*x1**2 + 0.5*x2**2 + 0.5*x3**2 + 0.5*x4**2 - 0.6",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -x1 - 0.4*x2 + 0.15*sin(x3) + u1, dx3/dt = x4 + u2, dx4/dt = -0.6*x3 - 0.3*x4 + u3",
        "initial_set": {
          "type": "box",
          "bounds": [
            [0.5, 0.8],
            [0.3, 0.6],
            [0.5, 0.8],
            [0.3, 0.6]
          ]
        },
        "unsafe_set": {
          "type": "union",
          "sets": [
            {
              "type": "box",
              "bounds": [
                [2.5, 3.5],
                [2.0, 3.0],
                [2.5, 3.5],
                [2.0, 3.0]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [-3.5, -2.5],
                [-3.0, -2.0],
                [-3.5, -2.5],
                [-3.0, -2.0]
              ]
            }
          ]
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "1.2*x1**2 + 1.5*x2**2 + 1.1*x3**2 + 1.4*x4**2 + 0.3*x1*x3 + 0.2*x2*x4 - 5.5",
      "controllers": "u0 = -1.5*x1 - 1.2*x2 - 0.2*x3, u1 = -0.8*x1 - 0.6*x2 + 0.1*x4, u2 = -1.4*x3 - 1.1*x4 - 0.2*x1, u3 = -0.7*x3 - 0.5*x4 + 0.1*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.1*x1 + 0.05*x2 + u0, dx2/dt = -0.05*x1 - 0.1*x2 + u1, dx3/dt = -0.2*x3 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 9",
      "controllers": "u0=-0.4*x1, u1=-0.4*x2, u2=-0.3*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.1*x1 + 0.05*x2, dx2/dt = -0.05*x1 - 0.1*x2, dx3/dt = -0.2*x3, dx4/dt = -0.3*x4, dx5/dt = -0.25*x5, dx6/dt = -0.15*x6",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0, 0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "0.8*x1**2 + 0.8*x2**2 + 1.2*x3**2 + 1.5*x4**2 + 1.3*x5**2 + 1.0*x6**2 - 9.0",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = sin(x1) + u1",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 1.5,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 1.0",
      "controllers": "u0=-3*x1 - 1.5*x2, u1=-3*x2 - 1.5*sin(x1)",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.4*x1 + 0.25*x2*x3 - 0.15*x1**3, dx2/dt = -0.5*x2 + 0.3*x1*x3 - 0.2*x2**3, dx3/dt = -0.6*x3 + 0.2*x1*x2 - 0.18*x1**2*x2",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 12",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 - x1**3 + u0, dx2/dt = -0.5*x1 - 0.3*x2 + u1",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 4",
      "controllers": "u0=-4*x1 - x2, u1=-x1 - 4*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.7*x1 + 0.1*x2, dx2/dt = -0.1*x1 - 0.8*x2, dx3/dt = -0.05*x1 - 1.0*x3, dx4/dt = -0.03*x2 - 1.1*x4",
        "initial_set": {
          "type": "ball",
          "radius": 0.7,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.8,
          "center": [0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 4.0",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.3*x1 + 0.2*x2*x4 - 0.15*x3**2, dx2/dt = -0.4*x2 + 0.25*x1*x3 - 0.18*x2*x4, dx3/dt = -0.5*x3 + 0.3*x1*x4 + 0.12*x2**2, dx4/dt = -0.6*x4 + 0.2*x2*x3 - 0.1*x1**2*x4",
        "initial_set": {
          "type": "ball",
          "radius": 0.4,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + 2*x3**2 + 3*x4**2 + 0.5*x1*x2 - 1",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1 + 0.1*x2, dx2/dt = -0.4*x2 + 0.1*x3, dx3/dt = -0.3*x3 + 0.1*x4, dx4/dt = -0.6*x4 + 0.1*x1",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 4.0,
          "center": [0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 4",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -5*x1 - 4*x2, dx2/dt = -x1 - 2*x2",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 - 4",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1 + 0.1*x2 + u0, dx2/dt = -0.4*x2 + 0.1*x3 + u1, dx3/dt = -0.3*x3 + 0.1*x4 + u2, dx4/dt = -0.6*x4 + 0.1*x1 + u3",
        "initial_set": {
          "type": "ball",
          "radius": 1.0,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 4.0,
          "center": [0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 12.25",
      "controllers": "u0=-0.6*x1 - 0.15*x2 - 0.15*x4, u1=-0.5*x2 - 0.15*x1 - 0.15*x3, u2=-0.7*x3 - 0.15*x2 - 0.15*x4, u3=-0.4*x4 - 0.15*x3 - 0.15*x1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -1*x1 + 4.5 + u0, dx2/dt = 1*x1 - 1*x2 - 3 + u1",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [1.75, 2.25],
            [1.75, 2.25]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [9, 10],
            [9, 10]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "(x1 - 3)**2 + (x2 - 3)**2 - 25",
      "controllers": "u0 = -2*x1 + 4.5, u1 = -2*x2 - x1 + 12",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 0.85*x1[k] + u0[k], x2[k+1] = 0.8*x2[k] + 0.15*x1[k] + u1[k]",
        "initial_set": {
          "type": "box",
          "bounds": [
            [1.5, 2.0],
            [1.2, 1.8]
          ]
        },
        "unsafe_set": {
          "type": "union",
          "sets": [
            {
              "type": "box",
              "bounds": [
                [4.5, 5.5],
                [4.0, 5.0]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [-5.5, -4.5],
                [-5.0, -4.0]
              ]
            }
          ]
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 8",
      "controllers": "u0 = -0.2*x1 - 0.1*x2, u1 = -0.1*x1 - 0.3*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.2*x1 - 0.1*(x1**2 - 1)*x2 + u1",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.8,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 6.25",
      "controllers": "u0=-4*x1 - 2*x2, u1=-4*x2 - 1.5*x1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 0.1*x1 - 0.02*x1*x2 + u0, dx2/dt = -0.15*x2 + 0.01*x1*x2 + u1",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [2.0, 3.0],
            [1.0, 2.0]
          ]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 8.0,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 25",
      "controllers": "u0=-0.5*x1 - 0.02*x1*(0.1 - 0.02*x2), u1=-0.5*x2 - 0.2*x2*(-0.15 + 0.01*x1)",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.3*x2 - 0.5*x1 - 0.1*x1**3 + u1",
        "initial_set": {
          "type": "ball",
          "radius": 0.8,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.2,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 10.24",
      "controllers": "u0=-x1 - 0.5*x2, u1=-0.7*x2 + 0.1*x1**3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -2.0*x1 - 0.8*x2 + u1",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [-0.5, 0.5],
            [-0.3, 0.3]
          ]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 5.0",
      "controllers": "u0=-2.0*x1 - 0.5*x2, u1=-1.0*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1 + 0.2*x2 + u0, dx2/dt = -0.3*x2 + 0.1*x1*x3 + u1, dx3/dt = -0.4*x3 - 0.05*x1*x2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 1.8,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 2.8",
      "controllers": "u0=-0.8*x1 - 0.2*x2, u1=-0.7*x2 - 0.1*x1*x3, u2=-0.6*x3 + 0.05*x1*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.6*x1 - 0.1*x2 + 0.05*x3 + u1, dx3/dt = x4 + u2, dx4/dt = -0.8*x3 - 0.15*x4 + 0.05*x1 + u3",
        "initial_set": {
          "type": "ball",
          "radius": 0.6,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 12",
      "controllers": "u0=-2*x1, u1=-2*x2, u2=-2*x3, u3=-2*x4",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.1*(x1 - 20) + 0.05*(x2 - x1) + u0, dx2/dt = -0.08*(x2 - 18) + 0.03*(x1 - x2) + u1",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [19.5, 20.5],
            [17.8, 18.2]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [25, 30],
            [25, 30]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "(x1 - 19)**2 + (x2 - 17.5)**2 - 30",
      "controllers": "u0 = -2.5*x1 - 0.5*x2 + 52, u1 = -0.4*x1 - 2.8*x2 + 58",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 1.0 - 0.5*x1 + u0, dx2/dt = 0.4*x1 - 0.3*x2 + u1, dx3/dt = 0.2*x2 - 0.1*x3 + u2",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.8, 1.2],
            [0.6, 1.0],
            [0.4, 0.8]
          ]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 5.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 20",
      "controllers": "u0 = -2*x1, u1 = -2*x2, u2 = -2*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -2.0*x1 + 1.5*x2 + u0, dx2/dt = -0.8*x2 + 0.6*x1 - 0.1*x1*x2 + u1",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 9.0",
      "controllers": "u0=-4.0*x1 - 2.0*x2, u1=-2.0*x1 - 3.0*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 0.5 - 0.2*x1 + u0, dx2/dt = 0.1*x1 - 0.15*x2 + u1, dx3/dt = 0.05*x2 - 0.1*x3 + u2",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [1.0, 1.5],
            [0.5, 1.0],
            [0.3, 0.7]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [4, 5],
            [3, 4],
            [2, 3]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "(x1 - 2.0)**2 + (x2 - 1.2)**2 + (x3 - 0.8)**2 - 2.25",
      "controllers": "u0 = -0.5 + 0.2*x1 - 0.8*(x1 - 2.0), u1 = -0.1*x1 + 0.15*x2 - 0.6*(x2 - 1.2), u2 = -0.05*x2 + 0.1*x3 - 0.4*(x3 - 0.8)",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.3*sin(x1) - 0.2*x2 + 0.1*x3 + u1, dx3/dt = x4 + u2, dx4/dt = -0.4*sin(x3) - 0.15*x4 + u3",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.0,
          "center": [0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 1",
      "controllers": "u0=-2*x1 - x2, u1=-x2 + 0.3*sin(x1) - 0.1*x3, u2=-2*x3 - x4, u3=-x4 + 0.4*sin(x3)",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1 + 0.3*x2*sin(x3) - 0.1*x1**2*x2, dx2/dt = -0.6*x2 + 0.5*x1*cos(x3) + 0.15*x3**2*x1, dx3/dt = -0.7*x3 - 0.1*x3**3",
        "initial_set": {
          "type": "ball",
          "radius": 0.4,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 2.25",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2, dx2/dt = -2.0*x1 - 0.8*x2, dx3/dt = -0.5*x3, dx4/dt = -0.3*x4, dx5/dt = -0.8*x5",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [-0.5, 0.5],
            [-0.3, 0.3],
            [-0.1, 0.1],
            [-0.1, 0.1],
            [-0.1, 0.1]
          ]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "3*x1**2 + x1*x2 + 2*x2**2 + 6*x3**2 + 8*x4**2 + 10*x5**2 - 1.5",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.3*x1 + 0.1*x2, dx2/dt = 0.2*x1 - 0.4*x2, dx3/dt = -0.7*x3, dx4/dt = -0.4*x4, dx5/dt = -0.6*x5, dx6/dt = -0.9*x6",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.8],
            [0.2, 0.9],
            [-0.1, 0.1],
            [-0.1, 0.1],
            [-0.1, 0.1],
            [-0.1, 0.1]
          ]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 + x5**2 + x6**2 - 2.5",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1, dx2/dt = -0.3*x2, dx3/dt = -0.8*x3, dx4/dt = -0.4*x4, dx5/dt = -0.9*x5, dx6/dt = -0.2*x6, dx7/dt = -0.6*x7",
        "initial_set": {
          "type": "ball",
          "radius": 0.8,
          "center": [0, 0, 0, 0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0, 0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "2*x1**2 + 3.33*x2**2 + 1.25*x3**2 + 2.5*x4**2 + 1.11*x5**2 + 5*x6**2 + 1.67*x7**2 - 4",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = x3 + u1, dx3/dt = -6*x3 - 2.92*x2 - 1.2*x1 + x1**2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.1,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 3.24",
      "controllers": "u0=-1.5*x1 - 0.8*x2, u1=-1.2*x2 - 1.8*x3, u2=4.8*x3 + 3.2*x2 + 2.0*x1 - 0.8*x1**2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.4*x1 + u0, dx2/dt = -0.5*x2 + 0.2*x1 + u1, dx3/dt = -0.6*x3 + 0.15*x2 + 0.1*x1*x2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.7,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 9",
      "controllers": "u0=-0.4*x1 - 0.1*x2 - 0.05*x2*x3, u1=-0.5*x2 - 0.2*x1 - 0.1*x1*x2, u2=-0.6*x3 - 0.15*x2 - 0.1*x1*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1 + 0.1*x2 + u0, dx2/dt = 0.1*x1 - 0.6*x2 + 0.1*x3 + u1, dx3/dt = 0.1*x2 - 0.7*x3 + 0.1*x4 + u2, dx4/dt = 0.1*x3 - 0.8*x4 + 0.1*x5 + u3, dx5/dt = 0.1*x4 - 0.9*x5 + 0.1*x6 + u4, dx6/dt = 0.1*x5 - 1.0*x6 + u5",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0, 0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3, u4, u5"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 + x5**2 + x6**2 - 8",
      "controllers": "u0=-0.8*x1, u1=-0.7*x2, u2=-0.9*x3, u3=-0.6*x4, u4=-1.1*x5, u5=-0.5*x6",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = x3 + u1, dx3/dt = -0.7*x3 - 0.1*x2 - 0.1*x1 + 0.1*x1**2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 1.0",
      "controllers": "u0=-x2 - 2.0*x1, u1=-x3 - 2.0*x2, u2=-2.0*x3 + 0.7*x3 + 0.1*x2 + 0.1*x1 - 0.1*x1**2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x1*(1 - x1 - 0.5*x2) + u0, dx2/dt = x2*(1 - x2 - 0.8*x1) + u1",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.5],
            [0.1, 0.5]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [0.8, 1.2],
            [0.8, 1.2]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "(x1 - 0.3)**2 + (x2 - 0.3)**2 - 0.16",
      "controllers": "u0 = -x1*(1 - x1 - 0.5*x2) - 1.5*(x1 - 0.3), u1 = -x2*(1 - x2 - 0.8*x1) - 1.5*(x2 - 0.3)",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -x1 + 0.08*x2 + x1**2*x2 + u0, dx2/dt = 0.6 - 0.08*x2 - x1**2*x2 + u1",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.5],
            [1.0, 2.0]
          ]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 5.0,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 9",
      "controllers": "u0=-3*x1 - 0.5*x1**3 - x1*x2**2, u1=-4*x2 - 1.2 - 0.3*x2**3 + 0.1*x1**2*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.1*x1 - 0.05*x2 + 0.02*x1*x3 + u1, dx3/dt = -0.2*x3 + 0.1*x1 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 8",
      "controllers": "u0=-x1 - 1.2*x2, u1=-x2 - 0.03*x1*x3, u2=-x3 - 0.15*x1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.25*x1 - x2**2 - x3**2 + 0.75 + u0, dx2/dt = -x2 + x1*x3 + u1, dx3/dt = -x3 + x1*x2 - 0.1*x1 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + 0.5*x1 - 2",
      "controllers": "u0 = -2.5*x1 + x2**2 + x3**2 - 1.5, u1 = -2.5*x2 - 0.7*x1*x3, u2 = -2.5*x3 - 0.7*x1*x2 + 0.12*x1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x1*(x1 - 0.1)*(1 - x1) - 0.3*x1*x2 + u0, dx2/dt = -0.2*x2 + 0.1*x1*x2 + u1",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.2, 0.8],
            [0.1, 0.6]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [1.5, 2.0],
            [1.0, 1.5]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 2.5",
      "controllers": "u0=-2.0*x1 - 0.5*x2, u1=-1.5*x2 - 0.4*x1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = x3 + u1, dx3/dt = -5.5*x3 - 3.5*x2 - x1 + x1**3 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 4.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "2*x1**2 + 2*x2**2 + x3**2 - 9",
      "controllers": "u0 = -2*x1 - x2, u1 = -x2 - 2*x3, u2 = -x1*x1*x1 - 2*x1 - 2*x2 - 6*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -x1 + x2*x3 + u1, dx3/dt = 1 - x2**2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 4",
      "controllers": "u0 = -2*x1, u1 = -2*x2, u2 = -2*x3 - 1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -x2 - x3 + u0, dx2/dt = x1 + 0.2*x2 + u1, dx3/dt = 0.2 + x3*(x1 - 5.7) + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.1,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 8.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "4*x1**2 + x2**2 + x3**2 - 16",
      "controllers": "u0 = x2 + x3 - 1.5*x1, u1 = -x1 - 1.5*x2, u2 = -0.2 - x3*(x1 - 5.7) - 2.0*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 36*(x2 - x1) + u0, dx2/dt = -x1*x3 + 20*x2 + u1, dx3/dt = x1*x2 - 3*x3 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.1,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 10.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 9",
      "controllers": "u0 = -40*x1 - 36*x2, u1 = -25*x2, u2 = -5*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1 + x2*x3 + u0, dx2/dt = -0.5*x2 + x3*(x1 - 1) + u1, dx3/dt = 1 - x1*x2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 4",
      "controllers": "u0=-6*x1 - x2*x3, u1=-6*x2 - x3*(x1-1), u2=-6*x3 - 1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -x1 + x2*x3 + u1, dx3/dt = 1 - x2**2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.4,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 1",
      "controllers": "u0 = -0.6*x1 - 0.6*x2, u1 = 0.6*x1 - 0.6*x2*x3 - 0.6*x2, u2 = -1 + x2**2 - 0.6*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = x1 - 0.5*x2 - x1*x3 + u1, dx3/dt = -1.5*x3 + x1**2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 6.0",
      "controllers": "u0=-2*x1 - x2, u1=-x1 - x2, u2=-2*x3 - x1**2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = x3 + u1, dx3/dt = -0.1*x3 - x2 - x1 + 0.5*x1**2 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 4.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 9",
      "controllers": "u0=-3*x1 - 0.5*x2, u1=-3*x2 - 0.5*x1, u2=-4*x3 - x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = 2*(x2 - x1) + 0.7*x4 + u0, dx2/dt = 1.5*x1 - x2 - x1*x3 + u1, dx3/dt = x1*x2 - 1.5*x3 + u2, dx4/dt = -x1 - 1.5*x4 + u3",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 4.0,
          "center": [0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 12.25",
      "controllers": "u0=-8*x1 - 0.5*x4, u1=-8*x2, u2=-8*x3, u3=0.5*x1 - 8*x4",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2*(x3 - 1 + x1**2) + 0.1*x1 + u0, dx2/dt = x1*(3*x3 + 1 - x1**2) + 0.1*x2 + u1, dx3/dt = -2*x3*(0.5 + x1*x2) + u2, dx4/dt = -0.5*x4 + u3",
        "initial_set": {
          "type": "ball",
          "radius": 0.1,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 8.0,
          "center": [0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 36",
      "controllers": "u0=-x2*(x3 - 1 + x1**2) - 0.7*x1, u1=-x1*(3*x3 + 1 - x1**2) - 0.7*x2, u2=2*x3*(0.5 + x1*x2) - 0.5*x3, u3=0.2*x4",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -x1 + 1.5*tanh(x2) - 1.3*tanh(x3) + u0, dx2/dt = -x2 + 1.2*tanh(x1) - 1.8*tanh(x3) + u1, dx3/dt = -x3 + 1.1*tanh(x1) + 0.1*tanh(x2) + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 8",
      "controllers": "u0=-2*x1 - 1.5*tanh(x2) + 1.3*tanh(x3), u1=-2*x2 - 1.2*tanh(x1) + 1.8*tanh(x3), u2=-2*x3 - 1.1*tanh(x1) - 0.1*tanh(x2)",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 0.92*x1[k] + 0.12*x2[k] + u0[k], x2[k+1] = -0.12*x1[k] + 0.92*x2[k] + u1[k], x3[k+1] = 0.88*x3[k] + u2[k]",
        "initial_set": {
          "type": "box",
          "bounds": [
            [1.0, 1.5],
            [0.8, 1.3],
            [0.6, 1.0]
          ]
        },
        "unsafe_set": {
          "type": "union",
          "sets": [
            {
              "type": "box",
              "bounds": [
                [3.5, 4.5],
                [3.0, 4.0],
                [2.5, 3.5]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [-4.5, -3.5],
                [-4.0, -3.0],
                [-3.5, -2.5]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [0.0, 0.5],
                [3.5, 4.0],
                [0.0, 0.5]
              ]
            }
          ]
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + 2*x3**2 - 8",
      "controllers": "u0 = -0.7*x1 - 0.2*x2 - 0.15*x3, u1 = 0.2*x1 - 0.7*x2 - 0.15*x3, u2 = -1.0*x3 - 0.1*x1 - 0.1*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.4*x1 + 0.05*x2, dx2/dt = -0.5*x2 + 0.05*x3, dx3/dt = -0.6*x3 + 0.05*x4, dx4/dt = -0.7*x4 + 0.05*x5, dx5/dt = -0.8*x5 + 0.05*x6, dx6/dt = -0.9*x6 + 0.05*x7, dx7/dt = -1.0*x7 + 0.05*x8, dx8/dt = -1.1*x8",
        "initial_set": {
          "type": "ball",
          "radius": 0.6,
          "center": [0, 0, 0, 0, 0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0, 0, 0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 + x5**2 + x6**2 + x7**2 + x8**2 - 4.0",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = x3 + u1, dx3/dt = -5*x3 - 3*x2 - x1 + 0.5*x1**3 + u2, dx4/dt = -0.8*x4 + u3, dx5/dt = -0.9*x5 + u4",
        "initial_set": {
          "type": "ball",
          "radius": 0.2,
          "center": [0, 0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3, u4"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 + x5**2 - 12",
      "controllers": "u0 = -2*x1, u1 = -2*x2, u2 = -x1 - x2 - x3, u3 = -x4, u4 = -x5",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.1*x1 - 0.5",
        "initial_set": {
          "type": "bounds",
          "bounds": [[1.0, 2.0]]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [[5.0, 6.0]],
          "complement": false
        }
      },
      "barrier": "x1 - 3.5",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x3 + x2*x1 + u0, dx2/dt = -x2 - x1**2 + u1, dx3/dt = -x1 - 0.5*x3 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.5,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 12",
      "controllers": "u0 = -2*x1, u1 = -x2, u2 = -2*x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.8*x1 - 0.3*x2*(1 + x1**2) + 0.1*x3 + u1, dx3/dt = x4 + u2, dx4/dt = -0.9*x3 - 0.25*x4*(1 + x3**2) + 0.1*x1 + u3",
        "initial_set": {
          "type": "ball",
          "radius": 0.35,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.8,
          "center": [0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 - 6.25",
      "controllers": "u0 = -0.4*x1*x2 - 0.8*x1, u1 = 0.2*x2*(1 + x1**2) - 0.05*x2*x3 - 0.8*x2, u2 = -0.05*x3*x4 - 0.8*x3, u3 = 0.15*x4*(1 + x3**2) - 0.05*x1*x4 - 0.8*x4",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.6*x1 + 0.15*x2*x3 + u0, dx2/dt = -0.7*x2 + 0.12*x1*x4 - 0.08*x3**2 + u1, dx3/dt = -0.8*x3 + 0.1*x2*x5 + 0.05*x1*x2 + u2, dx4/dt = -0.9*x4 + 0.08*x1*x3 - 0.06*x5**2 + u3, dx5/dt = -1.0*x5 + 0.1*x2*x4 + u4",
        "initial_set": {
          "type": "ball",
          "radius": 0.25,
          "center": [0, 0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.2,
          "center": [0, 0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3, u4"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 + x5**2 - 4.8",
      "controllers": "u0=-0.15*x2*x3 - 0.4*x1, u1=-0.12*x1*x4 + 0.08*x3**2 - 0.3*x2, u2=-0.1*x2*x5 - 0.05*x1*x2 - 0.2*x3, u3=-0.08*x1*x3 + 0.06*x5**2 - 0.1*x4, u4=-0.1*x2*x4 - 0.05*x5",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1 + 0.08*x2**2 + u0, dx2/dt = -0.6*x2 + 0.1*x1*x3 + 0.05*x4 + u1, dx3/dt = -0.7*x3 + 0.09*x2*x4 + 0.06*x5 + u2, dx4/dt = -0.8*x4 + 0.08*x3*x5 + 0.05*x6 + u3, dx5/dt = -0.9*x5 + 0.07*x4*x6 + 0.04*x1 + u4, dx6/dt = -1.0*x6 + 0.06*x5**2 + 0.05*x2 + u5",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.0,
          "center": [0, 0, 0, 0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2, u3, u4, u5"
      },
      "barrier": "x1**2 + x2**2 + x3**2 + x4**2 + x5**2 + x6**2 - 1.0",
      "controllers": "u0=-0.08*x2**2 - 0.1*x1, u1=-0.1*x1*x3 - 0.05*x4 - 0.1*x2, u2=-0.09*x2*x4 - 0.06*x5 - 0.1*x3, u3=-0.08*x3*x5 - 0.05*x6 - 0.1*x4, u4=-0.07*x4*x6 - 0.04*x1 - 0.1*x5, u5=-0.06*x5**2 - 0.05*x2 - 0.1*x6",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = x2 + u0, dx2/dt = -0.9*x1 - 0.4*x2 + u1, dx3/dt = -0.8*x3 + u2",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 1",
      "controllers": "u0 = -x1, u1 = -x2, u2 = -x3",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 0.87*x1[k] + 0.13*x2[k] + 0.06*x1[k]**2 + u0[k], x2[k+1] = -0.13*x1[k] + 0.87*x2[k] + u1[k], x3[k+1] = 0.85*x3[k] + 0.9*sin(x1[k]) + u2[k]",
        "initial_set": {
          "type": "box",
          "bounds": [
            [0.6, 1.0],
            [0.5, 0.9],
            [0.4, 0.8]
          ]
        },
        "unsafe_set": {
          "type": "union",
          "sets": [
            {
              "type": "box",
              "bounds": [
                [3.0, 4.0],
                [2.5, 3.5],
                [2.0, 3.0]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [-4.0, -3.0],
                [-3.5, -2.5],
                [-3.0, -2.0]
              ]
            },
            {
              "type": "box",
              "bounds": [
                [0.0, 0.5],
                [3.0, 3.5],
                [0.0, 0.5]
              ]
            }
          ]
        },
        "controller_parameters": "u0, u1, u2"
      },
      "barrier": "x1**2 + x2**2 + x3**2 - 2.5",
      "controllers": "u0 = -0.1*x1 - 0.06*x1**2, u1 = -0.1*x2, u2 = -0.2*x3 - 0.9*sin(x1)",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 0.95*x1[k] + 0.1*x2[k] + u0[k], x2[k+1] = -0.1*x1[k] + 0.95*x2[k] + u1[k]",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 3.5",
      "controllers": "u0 = -0.8*x1, u1 = -0.8*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = x1[k] + 0.01*(-100*x1[k] - x2[k]) + u0[k], x2[k+1] = x2[k] + 0.01*(x1[k] - 100*x2[k]) + u1[k]",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.4],
            [0.1, 0.55]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [0.45, 0.5],
            [0.6, 1]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 0.5",
      "controllers": "u0 = -0.3*x1 - 0.2*x2, u1 = -0.2*x1 - 0.4*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 0.8*x1[k] + 0.1*x1[k]**2 + 0.05*x2[k] + u0[k], x2[k+1] = 0.7*x2[k] + 0.1*x1[k]*x2[k] + u1[k]",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [-0.3, 0.3],
            [-0.2, 0.4]
          ]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 0.5",
      "controllers": "u0 = -0.2*x1 - 0.1*x1**2 - 0.05*x2, u1 = -0.1*x2 - 0.1*x1*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = x1[k]*(3.2 - 3.2*x1[k]) + u0[k], x2[k+1] = x2[k]*(2.8 - 2.8*x2[k]) + u1[k]",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.3],
            [0.2, 0.4]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [0.8, 1],
            [0.8, 1]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1 + x2 - 0.9",
      "controllers": "u0 = -x1*(2.2 - 3.2*x1) - 0.1, u1 = -x2*(1.8 - 2.8*x2) - 0.1",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 1 - 1.4*x1[k]**2 + x2[k] + u0[k], x2[k+1] = 0.3*x1[k] + u1[k]",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [-0.1, 0.1],
            [-0.1, 0.1]
          ]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2,
          "center": [0, 0],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1**2 + x2**2 - 1.0",
      "controllers": "u0 = -1 + 1.4*x1**2 - 0.5*x2, u1 = -0.3*x1 - 0.5*x2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = x1[k] + 0.01*(-100*x1[k] - 1*x2[k]), x2[k+1] = x2[k] + 0.01*(1*x1[k] - 100*x2[k])",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.4],
            [0.1, 0.55]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [0.45, 0.5],
            [0.6, 1]
          ],
          "complement": false
        }
      },
      "barrier": "x1**2 + x2**2 - 0.5",
      "template_type": "llm_generated"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 2.3*sin(x1[k]) + u0[k], x2[k+1] = 0.9*x2[k] + 0.1*sin(x1[k]) + u1[k]",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.5],
            [0.2, 0.4]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [2, 2.5],
            [1.5, 2]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1 + x2 - 0.9",
      "controllers": "u0 = x1 - 2.3*sin(x1) - 0.5, u1 = 0.1*x2 - 0.1*sin(x1) - 0.2",
      "template_type": "llm_generated_with_controller"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 1.2*sin(x1[k]) + u0[k], x2[k+1] = 0.88*x2[k] + u1[k]",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.5],
            [0.2, 0.4]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [2, 2.5],
            [1.5, 2]
          ],
          "complement": false
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": "x1 + x2 - 1.2",
      "controllers": "u0 = -1.2*sin(x1) + x1 - 0.05, u1 = 0.12*x2 - 0.05",
      "template_type": "llm_generated_with_controller"
    }
  ],
  "unsolved_problems": [
    {
      "problem": {
        "dynamics": "dx1/dt = -0.5*x1 + 0.3*x2, dx2/dt = -0.4*x2 + 0.15*cos(x1)*sin(x3), dx3/dt = -0.6*x3 + 0.1*sin(x2)*cos(x4), dx4/dt = -0.5*x4",
        "initial_set": {
          "type": "ball",
          "radius": 0.3,
          "center": [0, 0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 2.5,
          "center": [0, 0, 0, 0],
          "complement": true
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.3*x1 + 0.5*sin(x2), dx2/dt = -0.4*x2 - 0.6*sin(x1) + 0.1*sin(x3), dx3/dt = -0.5*x3 + 0.2*sin(x1)*sin(x2)",
        "initial_set": {
          "type": "ball",
          "radius": 0.4,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.0,
          "center": [0, 0, 0],
          "complement": true
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.3*x1 + 0.2*sin(x2)*exp(-x3**2), dx2/dt = -0.4*x2 + 0.15*cos(x1)*exp(-x1**2), dx3/dt = -0.5*x3 + 0.1*sin(x1 + x2)",
        "initial_set": {
          "type": "ball",
          "radius": 0.45,
          "center": [0, 0, 0]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 3.2,
          "center": [0, 0, 0],
          "complement": true
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 0.8*x1[k] + 0.1*sin(x2[k]), x2[k+1] = 0.85*x2[k] + 0.08*x1[k]*x3[k], x3[k+1] = 0.9*x3[k] + 0.08*cos(x1[k]*x2[k])",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.1, 0.4],
            [0.1, 0.3],
            [0.1, 0.4]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [2.0, 2.5],
            [1.8, 2.2],
            [1.8, 2.3]
          ],
          "complement": false
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.65*x1 + 0.1*x2**2*cos(x3), dx2/dt = -0.7*x2 + 0.12*sin(x1)*tanh(x4), dx3/dt = -0.75*x3 + 0.08*x1*x2, dx4/dt = -0.6*x4 + 0.06*(x1 + x2)",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [0.2, 0.5],
            [-0.3, 0.0],
            [0.1, 0.4],
            [-0.2, 0.1]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [-2.2, -1.7],
            [1.6, 2.1],
            [-1.9, -1.4],
            [1.3, 1.8]
          ],
          "complement": false
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.58*x1 + 0.12*sin(x2)*cos(x3), dx2/dt = -0.62*x2 + 0.1*exp(-x1**2)*tanh(x3), dx3/dt = -0.66*x3 + 0.08*sin(x1*x2)*exp(-x3**2)",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [-0.3, 0.2],
            [0.1, 0.4],
            [-0.2, 0.3]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [-2.3, -1.8],
            [1.7, 2.2],
            [-2.0, -1.5]
          ],
          "complement": false
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = u0*cos(x3), dx2/dt = u0*sin(x3), dx3/dt = u1",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [-1.0, 1.0],
            [-1.0, 1.0],
            [-0.5, 0.5]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [-5.0, 5.0],
            [-5.0, 5.0],
            [-3.14, 3.14]
          ],
          "complement": true
        },
        "controller_parameters": "u0, u1"
      },
      "barrier": null,
      "controllers": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 0.75*x1[k] + 0.1*tanh(x2[k])*tanh(x3[k]), x2[k+1] = 0.82*x2[k] + 0.09*sin(x1[k])*exp(-x3[k]**2), x3[k+1] = 0.79*x3[k] + 0.08*cos(x1[k])*cos(x2[k])",
        "initial_set": {
          "type": "ball",
          "radius": 0.5,
          "center": [1.0, -0.5, 0.8]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 0.6,
          "center": [-2.5, 2.0, -2.2],
          "complement": false
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "x1[k+1] = 0.73*x1[k] + 0.13*sin(x2[k])*tanh(x3[k]), x2[k+1] = 0.89*x2[k] + 0.17*cos(x1[k]**2)*exp(-x3[k]**2), x3[k+1] = 0.64*x3[k] + 0.22*tanh(x1[k]*x2[k])",
        "initial_set": {
          "type": "ball",
          "radius": 0.55,
          "center": [0.9, -0.7, 1.2]
        },
        "unsafe_set": {
          "type": "ball",
          "radius": 0.75,
          "center": [-3.1, 2.8, -2.6],
          "complement": false
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    },
    {
      "problem": {
        "dynamics": "dx1/dt = -0.62*x1 + 0.1*sin(x2 + x3), dx2/dt = -0.67*x2 + 0.08*cos(x1)*exp(-x3**2), dx3/dt = -0.64*x3 + 0.09*tanh(x1)*sin(x2)",
        "initial_set": {
          "type": "bounds",
          "bounds": [
            [-0.2, 0.3],
            [0.1, 0.5],
            [-0.3, 0.2]
          ]
        },
        "unsafe_set": {
          "type": "bounds",
          "bounds": [
            [2.0, 2.6],
            [-2.4, -1.8],
            [2.1, 2.7]
          ],
          "complement": false
        }
      },
      "barrier": null,
      "template_type": "unsolved"
    }
  ]
}