An Off-Line Formulation of Tube-Based Robust MPC Using Polyhedral Invariant Sets

Abstract

In this paper, an off-line formulation of tube-based robust model predictive control (MPC) using polyhedral invariant sets is proposed. A novel feature is the fact that no optimal control problem needs to be solved at each sampling time. Moreover, the proposed tube-based robust MPC algorithm can deal with the linear time-varying (LTV) system with bounded disturbance. The simulation results show that the state at each time step is restricted to lie within a tube whose center is the state of the nominal LTV system that converges to the origin. Finally, the state is kept within a tube whose center is at the origin, so robust stability is guaranteed. Satisfaction of the state and control constraints is guaranteed by employing tighter constraint sets for the nominal LTV system.

Keywords:

• Bounded disturbance
• Linear time-varying system
• Robust stability
• Tube-based robust MPC