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Finite Control Set Model Predictive Control with Limit Cycle Stability Guarantees

Duo Xu, Mircea Lazar

TL;DR

A FCS-MPC design that aims to stabilize a steady-state limit cycle compatible with a desired output reference via a suitable cost function and provides 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.

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.

Finite Control Set Model Predictive Control with Limit Cycle Stability Guarantees

TL;DR

A FCS-MPC design that aims to stabilize a steady-state limit cycle compatible with a desired output reference via a suitable cost function and provides 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.

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.
Paper Structure (12 sections, 76 equations, 9 figures, 1 table, 2 algorithms)

This paper contains 12 sections, 76 equations, 9 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Limit cycle existence and computation
  4. Limit cycle FCS-MPC
  5. Terminal ingredients design
  6. Recursive feasibility and limit cycle stability
  7. Computation of the terminal ingredients
  8. Computation of the terminal costs
  9. Computation of the terminal sets
  10. Polytopic outer approximation of $\mathbb{X}_f(N)$
  11. Illustrative Examples
  12. Conclusions

Figures (9)

  • Figure 1: Example 1: Ellipsoidal and polytopic periodic invariant sets.
  • Figure 2: Example 1: Closed-loop limit cycle FCS-MPC system behavior.
  • Figure 3: Example 1: Set of feasible states.
  • Figure 4: Example 1: State trajectory.
  • Figure 5: Schematic of the Buck Boost converter.
  • ...and 4 more figures