Hi Krishna,
To solve a convex Model Predictive Control (MPC) problem using the primal-dual interior-point method in MATLAB, you can set up the optimization problem in a form that can be solved by this method. Here's a simple example using MATLAB's built-in functions:
% Define the quadratic programming problem
Q = [2 0; 0 2]; % Positive definite matrix
c = [-2; -5]; % Linear term
% Inequality constraints
A = [-1 1; 1 2; 2 1];
b = [2; 6; 8];
% Equality constraints
Aeq = [1 1];
beq = [3];
% Initial guess
x0 = [0; 0];
% Options for the solver
options = optimoptions('quadprog', 'Algorithm', 'interior-point-convex', 'Display', 'iter');
% Solve the quadratic programming problem
[x, fval, exitflag, output] = quadprog(Q, c, A, b, Aeq, beq, [], [], x0, options);
% Display the results
disp('Optimal solution:');
disp(x);
disp('Optimal objective function value:');
disp(fval);
This example demonstrates how to set up and solve a convex quadratic programming problem using MATLAB's interior-point method. For a real-world Model Predictive Control (MPC) problem, you would need to define Q, c, A, b, Aeq, and beq based on your specific system dynamics, constraints, and cost function.
For more information on quadprog, refer to the following documentation link:
Hope this helps.
