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Distributed Data-driven Predictive Control via Dissipative Behavior Synthesis

Yitao Yan, Jie Bao, Biao Huang

TL;DR

This work develops a distributed data-driven predictive control framework for interconnected LTI subsystems within a behavioral systems theory setting. By treating dissipativity as a behavior and embedding QdF-based supply/storage in a virtual interconnection, the authors enable a unified, data-driven design that achieves network-wide performance through local QdF conditions and distributed optimization. Key contributions include finite-length interconnection results that allow recovery of the network behavior from local data, explicit dissipativity synthesis conditions with LMIs, and a practical DDPC procedure with consensus for scalable implementation. The approach yields provable guarantees on dissipativity and recursive feasibility, demonstrated via a numerical plant example. This provides a principled pathway for scalable, disturbance-attenuating control of large interconnected systems using only local data.

Abstract

This paper presents a distributed data-driven predictive control (DDPC) approach using the behavioral framework. It aims to design a network of controllers for an interconnected system with linear time-invariant (LTI) subsystems such that a given global (network-wide) cost function is minimized while desired control performance (e.g., network stability and disturbance rejection) is achieved using dissipativity in the quadratic difference form (QdF). By viewing dissipativity as a behavior and integrating it into the control design as a virtual dynamical system, the proposed approach carries out the entire design process in a unified framework with a set-theoretic viewpoint. This leads to an effective data-driven distributed control design, where the global design goal can be achieved by distributed optimization based on the local QdF conditions. The approach is illustrated by an example throughout the paper.

Distributed Data-driven Predictive Control via Dissipative Behavior Synthesis

TL;DR

This work develops a distributed data-driven predictive control framework for interconnected LTI subsystems within a behavioral systems theory setting. By treating dissipativity as a behavior and embedding QdF-based supply/storage in a virtual interconnection, the authors enable a unified, data-driven design that achieves network-wide performance through local QdF conditions and distributed optimization. Key contributions include finite-length interconnection results that allow recovery of the network behavior from local data, explicit dissipativity synthesis conditions with LMIs, and a practical DDPC procedure with consensus for scalable implementation. The approach yields provable guarantees on dissipativity and recursive feasibility, demonstrated via a numerical plant example. This provides a principled pathway for scalable, disturbance-attenuating control of large interconnected systems using only local data.

Abstract

This paper presents a distributed data-driven predictive control (DDPC) approach using the behavioral framework. It aims to design a network of controllers for an interconnected system with linear time-invariant (LTI) subsystems such that a given global (network-wide) cost function is minimized while desired control performance (e.g., network stability and disturbance rejection) is achieved using dissipativity in the quadratic difference form (QdF). By viewing dissipativity as a behavior and integrating it into the control design as a virtual dynamical system, the proposed approach carries out the entire design process in a unified framework with a set-theoretic viewpoint. This leads to an effective data-driven distributed control design, where the global design goal can be achieved by distributed optimization based on the local QdF conditions. The approach is illustrated by an example throughout the paper.
Paper Structure (26 sections, 21 theorems, 83 equations, 3 figures)

This paper contains 26 sections, 21 theorems, 83 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Behavioral Systems Theory
  4. Linear Time-Invariant Behaviors
  5. Behavioral Interconnections
  6. Dissipativity
  7. Problem Formulation
  8. Interconnection of Finite-Length Behaviors
  9. Dissipativity as Behavior
  10. Dissipative Dynamical Systems
  11. Interconnection with a Dissipative Dynamical System
  12. More on QdF-based Behaviors
  13. Distributed Control Design
  14. Preamble
  15. Existence of Desired Controlled Behavior
  16. ...and 11 more sections

Key Result

Lemma 1

Let $\Sigma$ be a time-invariant system. Let $\hat{w}_1,\hat{w}_2\in\mathfrak{B}_{|[1,L]}$ with $L>\mathtt{L}\left(\mathfrak{B}\right)$. If $\hat{w}_{1{|[L-l+1,L]}}=\hat{w}_{2{|[1,l]}}$, with $l\geq\mathtt{L}\left(\mathfrak{B}\right)$, then $\mathop{\mathrm{col}}\nolimits\left(\hat{w}_1,\hat{w}_{2{|

Figures (3)

  • Figure 1: Structure of the Controlled System
  • Figure 2: Illustrative Diagram of an Interconnected System with Distributed Controllers
  • Figure 3: Disturbance Profile and Controlled Outcome

Theorems & Definitions (39)

  • Lemma 1: Markovsky:2005
  • Lemma 2: Fundamental Lemma Willems:2005vanWaarde:2020
  • Remark 1
  • Lemma 3: Yan:2021
  • Example 1
  • Lemma 4
  • Theorem 5
  • proof
  • Remark 2
  • Corollary 6
  • ...and 29 more