Matlab program for convex MPC

16 views (last 30 days)
Krishna Kumar
Krishna Kumar on 12 Oct 2020
Answered: Shubham on 8 Nov 2024 at 8:38
how to solve an optimization problem in polynomial time by the primal dual interior point method with example.

Answers (1)

Shubham
Shubham on 8 Nov 2024 at 8:38
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);
The interior-point-convex algorithm does not accept an initial point. Ignoring X0. Iter Fval Primal Infeas Dual Infeas Complementarity 0 -6.720000e+00 3.996803e-15 5.600000e+00 2.800000e+00 1 -7.084989e+00 3.108624e-15 5.724830e-03 1.784682e-01 2 -7.124517e+00 1.776357e-15 2.862415e-06 1.532405e-02 3 -7.125000e+00 2.220446e-15 1.431207e-09 9.210425e-05 4 -7.125000e+00 8.881784e-16 7.156037e-13 4.606072e-08 5 -7.125000e+00 0.000000e+00 3.578877e-16 2.303035e-11 Minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.
% Display the results
disp('Optimal solution:');
Optimal solution:
disp(x);
0.7500 2.2500
disp('Optimal objective function value:');
Optimal objective function value:
disp(fval);
-7.1250
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.

Categories

Find more on Model Predictive Control Toolbox in Help Center and File Exchange

Products


Release

R2019b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!