Engineering_(Advanced_Control_Systems_Model_Predictive_Control_and_Robustness_Testing).ipynb

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        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# MPC parameters\n",
        "horizon = 5  # Prediction horizon\n",
        "dt = 0.1     # Time step\n",
        "setpoint = 1.0\n",
        "x = 0.0      # Initial state\n",
        "u = 0.0      # Control input\n",
        "\n",
        "# Define cost function for MPC\n",
        "def cost_function(x, u, setpoint, horizon, dt):\n",
        "    cost = 0.0\n",
        "    for _ in range(horizon):\n",
        "        error = setpoint - x\n",
        "        cost += error**2 + 0.01 * u**2  # Weighted sum of state and control effort\n",
        "        x = x + u * dt  # System dynamics\n",
        "    return cost\n",
        "\n",
        "# Simulation loop\n",
        "for _ in range(50):\n",
        "    best_u = min(np.linspace(-1, 1, 50), key=lambda u: cost_function(x, u, setpoint, horizon, dt))\n",
        "    x = x + best_u * dt\n",
        "    plt.plot(_, x, 'ro')\n",
        "plt.xlabel(\"Time step\")\n",
        "plt.ylabel(\"System state\")\n",
        "plt.title(\"MPC Response\")\n",
        "plt.show()"
      ]
    }
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