Finite Control Set Model Predictive Control with Limit Cycle Stability Guarantees

TL;DR

This paper introduces a finite control set model predictive control method that guarantees the stability of a desired steady-state limit cycle, improving predictability over existing approaches that only ensure practical stability.

Contribution

It proposes a novel FCS-MPC design that stabilizes limit cycles using periodic terminal costs and control laws, with systematic methods for computing invariant sets.

Findings

Guarantees asymptotic stability of limit cycles.

Ensures recursive feasibility with periodic terminal sets.

Validated on switched systems and power electronics benchmarks.

Abstract

This paper considers the design of finite control set model predictive control (FCS-MPC) for discrete-time switched affine systems. Existing FCS-MPC methods typically pursue practical stability guarantees, which ensure convergence to a bounded invariant set that contains a desired steady state. As such, current FCS-MPC methods result in unpredictable steady-state behavior due to arbitrary switching among the available finite control inputs. Motivated by this, we present a FCS-MPC design that aims to stabilize a steady-state limit cycle compatible with a desired output reference via a suitable cost function. We provide conditions in terms of periodic terminal costs and finite control set control laws that guarantee asymptotic stability of the developed limit cycle FCS-MPC algorithm. Moreover, we develop conditions for recursive feasibility of limit cycle FCS-MPC in terms of periodic terminal sets and we provide systematic methods for computing ellipsoidal and polytopic periodically invariant sets that contain a desired steady-state limit cycle. Compared to existing periodic terminal ingredients for tracking MPC with a continuous control set, we design and compute terminal ingredients using a finite control set. The developed methodology is validated on switched systems and power electronics benchmark examples.