Partial Enumeration MPC: Robust Stability Results and Application to an Unstable CSTR

Abstract

We revise in this paper the Partial Enumeration (PE) method for the fast computation of a suboptimal solution to linear MPC problems. We derive novel robust exponential stability results for difference inclusions to show that the existence of a continuous Lyapunov function implies Strong Robust Exponential Stability (SRES), i.e. for any sufficiently small perturbation. Given the fact that the suboptimal PE-based control law is non-unique and discontinuous, i.e. a set-valued map, we treat the closed-loop system, appropriately augmented, as a difference inclusion. Such approach allows us to show SRES of the closed-loop system under PE-based MPC. Application to a simulated open-loop unstable CSTR is presented to show the performance and timing results of PE-based MPC, as well as to highlight its robustness to process/model mismatch, disturbances and measurement noise.