A primal-dual interior-point linear programming algorithm for MPC

Constrained optimal control problems for linear systems with linear constraints and an objective function consisting of linear and l1-norm terms can be expressed as linear programs. We develop an efficient primal-dual interior point algorithm for solution of such linear programs. The algorithm is implemented in Matlab and its performance is compared to an active set based LP solver and linprog in Matlab's optimization toolbox. Simulations demonstrate that the new algorithm is more than one magnitude faster than the other LP algorithms applied to this problem.