Time optimal MPC based on offline construction of ellipsoidal sets

A time optimal model predictive control (MPC) strategy is proposed in the paper. It makes use of a dual mode strategy and a quasi-closed loop control law. A series of ellipsoidal sets can be constructed offline to describe the t-step feasible region. For linear parameter varying system, a step by step backwards computation method is developed, and this renders that the recursive feasibility and stability can be guaranteed. The time optimal MPC algorithm only needs to judge a series of inequalities online and thus reduces the computational burden greatly in contrast with the existing algorithms, which are required to check a number of feasibility problems online. Numerical examples are used to illustrate the effectiveness of the proposed strategy.