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Novel Multi-objective Switched Model Predictive Control with Feasibility and Stability Guarantees

Elias Niepötter, Adrian Grimm, Torbjørn Cunis

TL;DR

The paper addresses multi-objective control under switching by introducing a parallel-$pSMPC$ framework with a supervisory switching mechanism. It presents two rigorously guaranteed frameworks: a nominal Leader-Restrictor approach ensuring recursive feasibility and stability via a Lyapunov-based switching condition, and a robust ISS-based framework incorporating disturbance handling through an ISS-Lyapunov formulation. A composed OCP and constructive switching laws guarantee recursive feasibility for arbitrary switching; the robust version guarantees ISS with respect to disturbances. A numerical example on linear aircraft longitudinal dynamics demonstrates superior performance of the proposed pSMPC over standard QIH-MPC, illustrating practical applicability to distributed and multi-objective control tasks.

Abstract

As the relevance of control systems capable of dealing with multiple objectives rises (e.g. being economic while maintaining a certain performance), multi-objective Switched Model Predictive Control combines all the advantages of Model Predictive Control while dealing with multiple objectives. We propose two novel frameworks, a nominal and a robust framework to guarantee recursive feasibility of each Model Predictive Controller under arbitrary switching and assure asymptotic stability of the closed-loop system applying the nominal framework and Input-to-State stability using the robust framework. The presented frameworks employ methods from switched systems, enabling the utilization of a supervisor control instance which allows for complex objectives and multi-objective control. Our numerical example confirms the superior performance of our proposed frameworks compared to a standard Model Predictive Control approach.

Novel Multi-objective Switched Model Predictive Control with Feasibility and Stability Guarantees

TL;DR

The paper addresses multi-objective control under switching by introducing a parallel- framework with a supervisory switching mechanism. It presents two rigorously guaranteed frameworks: a nominal Leader-Restrictor approach ensuring recursive feasibility and stability via a Lyapunov-based switching condition, and a robust ISS-based framework incorporating disturbance handling through an ISS-Lyapunov formulation. A composed OCP and constructive switching laws guarantee recursive feasibility for arbitrary switching; the robust version guarantees ISS with respect to disturbances. A numerical example on linear aircraft longitudinal dynamics demonstrates superior performance of the proposed pSMPC over standard QIH-MPC, illustrating practical applicability to distributed and multi-objective control tasks.

Abstract

As the relevance of control systems capable of dealing with multiple objectives rises (e.g. being economic while maintaining a certain performance), multi-objective Switched Model Predictive Control combines all the advantages of Model Predictive Control while dealing with multiple objectives. We propose two novel frameworks, a nominal and a robust framework to guarantee recursive feasibility of each Model Predictive Controller under arbitrary switching and assure asymptotic stability of the closed-loop system applying the nominal framework and Input-to-State stability using the robust framework. The presented frameworks employ methods from switched systems, enabling the utilization of a supervisor control instance which allows for complex objectives and multi-objective control. Our numerical example confirms the superior performance of our proposed frameworks compared to a standard Model Predictive Control approach.

Paper Structure

This paper contains 16 sections, 5 theorems, 29 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Contribution
  4. Preliminaries
  5. Control Structure
  6. Nominal and Robust Model Predictive Control
  7. Switched Systems Stability
  8. Main Results
  9. Nominal: Leader-Restrictor Framework
  10. Robust: Multiple ISS-Lyapunov Functions
  11. Discussion
  12. Numerical Example
  13. Setup
  14. Supervisor Objective
  15. Results
  16. ...and 1 more sections

Key Result

Lemma 1

Let $V_i$ denote a Lyapunov function corresponding to the $i$-th system of the family eq:switchedSystem where $\boldsymbol{\nu} = 0$. Assume that there exist p.d. functions $W_i: \mathbb R^{n_i} \to \mathbb R$ for all $i \in \mathcal{I}$. The switched system eq:switchedSystem is globally asymptotica for all $i \in \mathcal{I}$.

Figures (4)

  • Figure 1: Overview of the control structure inspired by parisini_hybrid_rhc
  • Figure 2: Deviation of the energy over time for all four control schemes (nominal).
  • Figure 3: Switching signal and permission (nominal).
  • Figure 4: Switching signal and permission (robust).

Theorems & Definitions (13)

  • Lemma 1
  • Definition 1
  • Definition 2
  • Proposition 1
  • proof
  • Lemma 2
  • proof
  • Remark 1
  • Remark 2
  • Theorem 1
  • ...and 3 more