A Lyapunov-based model predictive control with DSMC as an auxiliary control to facilitate stability

Abstract

In this study, we propose a Lyapunov-based model predictive control (LMPC) framework combined with discrete-time sliding mode control (DSMC) as an auxiliary control for the discrete-time systems with input saturations. An anti-windup auxiliary variable is introduced in DSMC to handle control input saturations. A Lyapunov function decay stability constraint is proposed to guarantee the stability of closed-loop system and the recursive feasibility of the optimization problem. The finite time open-loop optimization problem of LMPC is transformed into quadratic programming solved by interior-point method. It is more practical to establish the LMPC framework in the discrete time domain, that is, DSMC and MPC are both conducted in the discrete-time domain. As the DSMC takes control saturation into account, the close-loop system stability of the LMPC is rigorously proved without various harsh assumptions or condition. Finally, a numerical example and a path tracking control example of autonomous vehicles are employed to demonstrate that the proposed LMPC leads to superior error convergence properties and enlarged feasible region.