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Coalitional control: a bottom-up approach

Filiberto Fele, José M. Maestre, Eduardo F. Camacho

TL;DR

The paper addresses scalability and communication challenges in large-scale, interconnected control systems by proposing a bottom-up coalitional control framework where control agents form coalitions online based on time-varying interconnections. It introduces two bargaining schemes, Coalitional Cooperative (COO) and Coalitional Individually Rational (CIR), to decide when to merge subsystems and how to allocate costs using a Shapley-value approach, ensuring individual rationality. A joint MPC formulation for coalitions is defined, incorporating cooperation costs and merged dynamics, and decisions hinge on the condition $J_{12}^* \le J_1^* + J_2^*$ (and, for CIR, on Shapley-based allocations). The framework is evaluated on a 4x4 storage network, showing that autonomous coalitions can achieve performance between centralized and decentralized control, with cooperation rates adapting as the system nears the setpoint; the work also bridges distributed control with cooperative game theory, offering a scalable approach for dynamically evolving coalitions in complex systems.

Abstract

The recent major developments in information technologies have opened interesting possibilities for the effective management of multi-agent systems. In many cases, the important role of central control nodes can now be undertaken by several controllers in a distributed topology that suits better the structure of the system. This opens as well the possibility to promote cooperation between control agents in competitive environments, establishing links between controllers in order to adapt the exchange of critical information to the degree of subsystems' interactions. In this paper a bottom-up approach to coalitional control is presented, where the structure of each agent's model predictive controller is adapted to the time-variant coupling conditions, promoting the formation of coalitions - clusters of control agents where communication is essential to ensure the cooperation - whenever it can bring benefit to the overall system performance.

Coalitional control: a bottom-up approach

TL;DR

The paper addresses scalability and communication challenges in large-scale, interconnected control systems by proposing a bottom-up coalitional control framework where control agents form coalitions online based on time-varying interconnections. It introduces two bargaining schemes, Coalitional Cooperative (COO) and Coalitional Individually Rational (CIR), to decide when to merge subsystems and how to allocate costs using a Shapley-value approach, ensuring individual rationality. A joint MPC formulation for coalitions is defined, incorporating cooperation costs and merged dynamics, and decisions hinge on the condition (and, for CIR, on Shapley-based allocations). The framework is evaluated on a 4x4 storage network, showing that autonomous coalitions can achieve performance between centralized and decentralized control, with cooperation rates adapting as the system nears the setpoint; the work also bridges distributed control with cooperative game theory, offering a scalable approach for dynamically evolving coalitions in complex systems.

Abstract

The recent major developments in information technologies have opened interesting possibilities for the effective management of multi-agent systems. In many cases, the important role of central control nodes can now be undertaken by several controllers in a distributed topology that suits better the structure of the system. This opens as well the possibility to promote cooperation between control agents in competitive environments, establishing links between controllers in order to adapt the exchange of critical information to the degree of subsystems' interactions. In this paper a bottom-up approach to coalitional control is presented, where the structure of each agent's model predictive controller is adapted to the time-variant coupling conditions, promoting the formation of coalitions - clusters of control agents where communication is essential to ensure the cooperation - whenever it can bring benefit to the overall system performance.

Paper Structure

This paper contains 7 sections, 22 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Coalitional control schemes
  4. Coalitional Cooperative algorithm
  5. Coalitional Individually Rational algorithm
  6. Simulations
  7. Conclusions

Figures (2)

  • Figure 1: Evolution of the states for the control schemes considered.
  • Figure 2: Evolution of the coalitions produced by the COO algorithm, with cooperation costs expressed as $(b)$. The cooperation between subsystems is promoted in order to improve their MPC performance index and, as a consequence, the overall system is driven towards its setpoint. As the cost decreases, the cooperation rate is reduced.

Theorems & Definitions (1)

  • Remark 1