Constrained time-optimal control of linear parameter-varying systems

For linear and hybrid systems, constrained time-optimal control was shown to be a low complexity alternative to the explicit solution of the constrained finite-time optimal control problem. In this paper we show how Polya´s relaxation can be employed to compute minimum-time controllers for discrete-time LPV systems. Contrary to previous publications, our approach allows the use of parameter-varying input matrices. In a comparison over 20 random system, it is shown that compared to explicit LPV-MPC the proposed approach achieves similar or even better control performance, while reducing the complexity of the controller up to an order of magnitude.