build a nonlinear robust mpc in matlab in matlab

To build a nonlinear robust Model Predictive Control (MPC) in Matlab, you can follow the steps below:

1. Define the Nonlinear System: Define the plant model as a set of nonlinear state-space equations. You can use Simulink or create the model using equations directly in Matlab.

2. Linearize the System: Linearize the nonlinear system about the operating point to obtain a linearized state-space model. This model will be used as a basis for the MPC controller design.

3. Design the Robust MPC Controller: Use the linearized model to design an MPC controller using the "mpc" function in Matlab. The "mpc" function allows for the specification of constraints and weights that are used to optimize the control action. Additionally, you can use the "robustMPC" object in Matlab to design a robust MPC controller that can handle plant uncertainties.

Here is an example code snippet that shows how to design a robust nonlinear MPC controller in Matlab:

main.m
% Define the nonlinear system
model = @(x,u) [x(1) + u^2; x(2) - u^3]; 

% Linearize the system about the operating point
x0 = [1; 1];
u0 = 0;
[A, B] = jacobianest(model, x0, u0);

% Define the MPC controller
Ts = 0.1;
mpcobj = mpc(ss(A, B, eye(2), 0), Ts);

% Set controller constraints and weights
mpcobj.MV(1).Min = -10;
mpcobj.MV(1).Max = 10;
mpcobj.Weights.MV = 0.1;
mpcobj.Weights.MVRate = 0.2;
mpcobj.Weights.OV = [1 1];

% Design robust MPC controller
robustmpc = robustMPC(mpcobj, [], [], [], [], 'MonteCarlo', 50);

% Simulate the system with the MPC controller
T = 10;
x = [1; 1];
u = 0;
for k = 1:T/Ts
    u = robustmpc.evaluate(x);
    x = model(x, u);
end
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This code defines a simple nonlinear model and linearizes it. Then, it defines an MPC controller object and sets constraints and weights for the optimization problem. Finally, it uses the "robustMPC" function to design a robust MPC controller that can handle plant uncertainties. The controller is then used to simulate the system over a period of time.