Robust model predictive control by iterative optimisation for polytopic uncertain systems

Abstract

This article addresses robust model predictive control (MPC) for constrained systems with polytopic uncertainty description. Firstly, in the technique which parametrises the infinite horizon control moves into a single state feedback law and invokes the parameter-dependent Lyapunov method for achieving closed-loop stability, the slack matrices are iteratively solved at each sampling time. Secondly, in the technique which parametrises the infinite horizon control moves into a set of free perturbations followed by a single state feedback law, the feedback gains within the switch horizon are iteratively found at each sampling time, rather than just inherited from the previous sampling time. Numerical examples show that iterative MPC can not only improve the control performance, but also enlarge the region of attraction.

Keywords:

• model predictive control
• uncertain systems
• iterative optimisation
• slack matrix
• feedback gain