An interpolation-based robust MPC algorithm using polyhedral invariant sets

This article presents an interpolation-based robust MPC algorithm for uncertain polytopic discrete-time systems using polyhedral invariant sets. Two nested polyhedral invariant sets are constructed off-line by solving robust constrained model predictive control optimization problems. The first one is a large set constructed to cover all of the desired operating spaces. The second one is a small target set constructed to drive the terminal state into. The real-time control law is calculated by linear interpolation between the two state feedback gains corresponding to these nested precomputed polyhedral invariant sets. At each sampling instant, only a computationally low-demanding optimization problem is needed to be solved on-line. The controller design is illustrated with an example. The proposed algorithm can achieve good control performance while on-line computation is still tractable.