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Network-Realised Model Predictive Control Part I: NRF-Enabled Closed-loop Decomposition

Andrei Sperilă, Alessio Iovine, Sorin Olaru, Patrick Panciatici

TL;DR

This paper presents a scalable, two-layer control architecture for constraint-based decision-making in networks by leveraging Network Realisation Function (NRF) based controllers in the first layer. The NRF design yields sparse, area-local state-space realizations and fully parameterised closed-loop maps via a tunable Q, enabling offline model-matching to decouple network areas and simplify online supervisory control. A detailed model-matching formulation and solution strategy are provided to achieve desired inter-area decoupling, with a complete numerical demonstration on a 5-node power-grid benchmark illustrating reduced online complexity and robust decoupling performance. The work lays the groundwork for a companion paper that completes the two-layer framework by detailing the second-layer MPC-based constraint management and inter-layer interfacing. Overall, the approach offers a flexible, offline-first decomposition that enhances scalability for distributed MPC-like strategies in large networks.

Abstract

A two-layer control architecture is proposed, which promotes scalable implementations for constraint-based decision strategies, such as model predictive controllers. The bottom layer is based upon a distributed feedback-feedforward scheme, which directs the controlled network's information flow according to a pre-specified communication infrastructure. Explicit expressions for the resulting closed-loop maps are obtained, and an offline model-matching procedure is proposed for designing the first layer. The obtained control laws are deployed via distributed state-space-based implementations, and the resulting closed-loop models enable predictive control design for the constraint management procedure described in our companion paper.

Network-Realised Model Predictive Control Part I: NRF-Enabled Closed-loop Decomposition

TL;DR

This paper presents a scalable, two-layer control architecture for constraint-based decision-making in networks by leveraging Network Realisation Function (NRF) based controllers in the first layer. The NRF design yields sparse, area-local state-space realizations and fully parameterised closed-loop maps via a tunable Q, enabling offline model-matching to decouple network areas and simplify online supervisory control. A detailed model-matching formulation and solution strategy are provided to achieve desired inter-area decoupling, with a complete numerical demonstration on a 5-node power-grid benchmark illustrating reduced online complexity and robust decoupling performance. The work lays the groundwork for a companion paper that completes the two-layer framework by detailing the second-layer MPC-based constraint management and inter-layer interfacing. Overall, the approach offers a flexible, offline-first decomposition that enhances scalability for distributed MPC-like strategies in large networks.

Abstract

A two-layer control architecture is proposed, which promotes scalable implementations for constraint-based decision strategies, such as model predictive controllers. The bottom layer is based upon a distributed feedback-feedforward scheme, which directs the controlled network's information flow according to a pre-specified communication infrastructure. Explicit expressions for the resulting closed-loop maps are obtained, and an offline model-matching procedure is proposed for designing the first layer. The obtained control laws are deployed via distributed state-space-based implementations, and the resulting closed-loop models enable predictive control design for the constraint management procedure described in our companion paper.

Paper Structure

This paper contains 36 sections, 3 theorems, 77 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Context
  3. Motivation
  4. Scope of Work
  5. Contributions
  6. Paper Structure
  7. Preliminaries
  8. Notation and Definitions
  9. System Representations
  10. Distributed Networks
  11. The Control Architecture
  12. Global Perspective and Objectives
  13. Fundamentals of NRF-based Control
  14. Objectives of the First Layer
  15. Theoretical Results
  16. ...and 21 more sections

Key Result

Proposition 4.1

Let the rows of the TFM from eq:Kd_def be described by the minimal realisations for which we define the polynomials Then, by expressing the aforementioned row TFMs as we have that:

Figures (5)

  • 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 implementation $\mathbf{K}_{\bf \mathbf{D}}(z)$
  • Figure 3: Implementation scheme for the $i^\text{th}$ area's NRF-based subcontroller
  • Figure 4: The $i^\text{th}$ area's desired closed-loop response, as designated by the choice of TFMs in \ref{['eq:des_d_a']}-\ref{['eq:des_c_d']}.
  • Figure 5: Interconnection topology of the grid's dynamics

Theorems & Definitions (31)

  • Remark 1.1
  • Remark 1.2
  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 3.1
  • Remark 3.2
  • Remark 3.3
  • Remark 3.4
  • Remark 3.5
  • ...and 21 more