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Network-Realised Model Predictive Control Part II: Distributed Constraint Management

Andrei Sperilă, Alessio Iovine, Sorin Olaru, Patrick Panciatici

TL;DR

This work introduces a two-layer Network Realised Model Predictive Control framework for distributed constraint management in networked systems. The first layer employs NRF-based controllers to achieve robust disturbance rejection and reference tracking, while the second layer provides a distributed MPC that enforces state and input constraints via area-based prediction models and set-based feasibility. Global guarantees, including recursive feasibility and constraint satisfaction, arise from careful decomposition into areas, disturbance modeling, and offline design of polyhedral inner-approximations, enabling fully distributed online optimization. A vehicle platoon numerical example demonstrates near-uninterrupted constraint satisfaction with minimal second-layer intervention, underscoring the practical scalability and robustness of the architecture for large networks.

Abstract

A two-layer control architecture is proposed, which promotes scalable implementations for model predictive controllers. The top layer acts as both a reference governor for the bottom layer and as a feedback controller for the regulated network. By employing set-based methods, global theoretical guarantees are obtained by enforcing local constraints upon the network's variables and upon those of the first layer's implementation. The proposed technique offers recursive feasibility guarantees as one of its central features, and the expressions of the resulting predictive strategies bear a striking resemblance to classical formulations from model predictive control literature, allowing for flexible and easily customisable implementations.

Network-Realised Model Predictive Control Part II: Distributed Constraint Management

TL;DR

This work introduces a two-layer Network Realised Model Predictive Control framework for distributed constraint management in networked systems. The first layer employs NRF-based controllers to achieve robust disturbance rejection and reference tracking, while the second layer provides a distributed MPC that enforces state and input constraints via area-based prediction models and set-based feasibility. Global guarantees, including recursive feasibility and constraint satisfaction, arise from careful decomposition into areas, disturbance modeling, and offline design of polyhedral inner-approximations, enabling fully distributed online optimization. A vehicle platoon numerical example demonstrates near-uninterrupted constraint satisfaction with minimal second-layer intervention, underscoring the practical scalability and robustness of the architecture for large networks.

Abstract

A two-layer control architecture is proposed, which promotes scalable implementations for model predictive controllers. The top layer acts as both a reference governor for the bottom layer and as a feedback controller for the regulated network. By employing set-based methods, global theoretical guarantees are obtained by enforcing local constraints upon the network's variables and upon those of the first layer's implementation. The proposed technique offers recursive feasibility guarantees as one of its central features, and the expressions of the resulting predictive strategies bear a striking resemblance to classical formulations from model predictive control literature, allowing for flexible and easily customisable implementations.

Paper Structure

This paper contains 44 sections, 3 theorems, 78 equations, 10 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Setting and Context
  3. Motivation
  4. Scope of Work
  5. Contribution
  6. Paper Structure
  7. Preliminaries
  8. Notation and Definitions
  9. System Representations
  10. Distributed Networks
  11. The Control Architecture
  12. Global Perspective and Functioning
  13. Objectives of the MPC Layer
  14. Obtaining an MPC-Oriented Formulation
  15. Interfacing with the First Layer
  16. ...and 29 more sections

Key Result

Proposition 5.1

Let the first-layer subcontrollers be implemented as in eq:Kd_def-eq:dist_implem. For each $i\in\{1:N\}$, define ${Z}_{ri}:=\mathrm{diag}(S_{ui},S_{xi})$ along with the sets from eq:feedback_set and eq:NRF_state_sets_a-eq:NRF_state_sets_b, which are located at the top of this page. Assume, moreover, given some $k_0\in\mathbb{N}$. Then, $\forall\,i\in\{1:N\}$, we have that:

Figures (10)

  • Figure 1: High-level implementation scheme depicting the proposed distributed control strategy
  • Figure 2: Feedback loop of a network's model ${\bf G}(z)$ with the NRF-based distributed implementation $\mathbf{K}_{\bf \mathbf{D}}(z)$
  • Figure 3: $0^{th}$ car speed and speeds of the platoon's cars
  • Figure 4: Length-based interdistances of the platoon's cars
  • Figure 5: Outputs of the first-layer subcontrollers
  • ...and 5 more figures

Theorems & Definitions (28)

  • Remark 2.1
  • Remark 3.1
  • Remark 3.2
  • Remark 4.1
  • Remark 4.2
  • Remark 4.3
  • Remark 4.4
  • Remark 4.5
  • Remark 5.1
  • Remark 5.2
  • ...and 18 more