Time optimal model predictive control for linear systems based on ellipsoidal and polytopic sets

Time optimal model predictive control (MPC) strategies are investigated in this paper. We first derive a series of controllable sets described by ellipsoids or convex polytopes offline, then obtain the control input that can steer initial state into the terminal set in the shortest time steps by solving an online optimisation problem with lower computational burden. The constraints of online optimisation problem are determined by the controllable sets. We give the methods to calculate the ellipsoidal controllable sets for linear time-invariant systems and linear time-varying systems, respectively, and propose a new method to calculate the polytopic controllable sets for linear time-varying systems. The recursive feasibility of online optimisation problem and the stability of the closed-loop system can be guaranteed. Numerical examples show that the algorithms work well.