Tube-based Robust MPC for Linear Time-Varying Systems with Bounded Disturbances

In this paper, a novel synthesis approach for tube-based robust MPC is proposed. A novel feature is the fact that the proposed tube-based robust MPC algorithm can deal with both time-varying parameter and bounded disturbance. The proposed control law is the linear combination of two components. The first component steers the state of the nominal linear time-varying system to the origin. The second component keeps the state at each time step of the linear time-varying system with bounded disturbance within a tube whose center is the state of the nominal linear time-varying system. Finally, the state of the linear time-varying system with bounded disturbance is kept within a tube whose center is at the origin so robust stability is guaranteed. Satisfaction of the state and control constraints is ensured by employing tighter constraint sets for the nominal linear time-varying system. The computational burdens are the same as those in the case of the nominal linear time-varying system.