Partial enumeration MPC: Robust stability results and application to an unstable CSTR

Abstract

We describe a partial enumeration (PE) method for fast computation of a suboptimal solution to linear MPC problems [1] with robust stability properties. Given that the suboptimal PE-based control law is non-unique (that is, a set-valued map) and (possibly) discontinuous, we treat the closed-loop system, appropriately augmented, as a difference inclusion. We derive novel robust exponential stability results for difference inclusions of this type. In particular we show that Strong Robust Exponential Stability (SRES) holds, for any sufficiently small but otherwise arbitrary perturbation. Such approach allows us to show SRES of the closed-loop system under PE-based MPC. Application to a simulated open-loop unstable CSTR with separation unit and recycle is presented to show performance and timing results for PE-based MPC, as well as to highlight its robustness to process/model mismatch, disturbances and measurement noise.