nonlinear model predictive control in matlab

Nonlinear Model Predictive Control (NMPC) can be implemented in MATLAB using the built-in Optimization Toolbox. The basic steps involved in implementing NMPC are:

1. Define the system dynamics and constraints: This involves defining the equations that describe the behavior of the system under control, as well as any physical or operational constraints that must be satisfied.

2. Formulate the optimization problem: This involves defining the objective function that is to be optimized subject to the system dynamics and constraints.

3. Solve the optimization problem: This involves using the Optimization Toolbox to solve the optimization problem defined in step 2.

4. Update the control inputs: This involves applying the control inputs obtained from the solution of the optimization problem to the system under control, and then repeating the process from step 1.

Here is an example MATLAB code that implements NMPC for a simple nonlinear system:

main.m
% Define the system dynamics and constraints
x0 = [1; 0]; tspan = [0 10];
odefun = @(t,x,u) [x(1) - x(1)*x(2) + u; -x(2) + x(1)*x(2)];
uconstraints = [-1.5 1.5];

% Define the optimization problem
optfcn = @(u) nmpcobjfcn(u,tspan,x0,odefun,@nmpcconstrfcn,uconstraints);
nvars = 10; lb = uconstraints(1)*ones(nvars,1); ub = uconstraints(2)*ones(nvars,1);
opts = optimoptions('fmincon','Algorithm','interior-point','MaxIterations',500);
u0 = linspace(uconstraints(1),uconstraints(2),nvars)';
[uopt,fopt] = fmincon(optfcn,u0,[],[],[],[],lb,ub,[],opts);

% Update the control inputs
u = uopt(1);
[t,x] = ode45(@(t,x) odefun(t,x,u),tspan,x0);
plot(t,x(:,1));
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In this code, the odefun function defines the system dynamics, and the nmpcobjfcn and nmpcconstrfcn functions define the objective function and constraints for the optimization problem. The fmincon function is used to solve the optimization problem, and the resulting control input uopt is applied to the system using the ode45 function.