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A distributed framework for linear adaptive MPC

Anilkumar Parsi, Ahmed Aboudonia, Andrea Iannelli, John Lygeros, Roy S. Smith

TL;DR

This work tackles the scalability and decentralization challenges of adaptive MPC for interconnected networks by proposing a distributed adaptive MPC (DAMPC) framework. It imposes a structured optimization design and employs ADMM to solve the online MPC problem in a distributed fashion, while enabling online set-membership identification in both decentralized and distributed forms. The main contributions are (i) a linear-growth, distributed optimization formulation with block-diagonal costs and neighbor-constrained interactions, (ii) two identification schemes that tighten parameter bounds without a central unit, and (iii) guarantees of robust constraint satisfaction, recursive feasibility, and finite-gain $\ell_2$ stability, demonstrated on an uncertain mass-spring-damper network. The results show that adapting parameters via distributed identification yields meaningful cost reductions compared to a non-adaptive distributed robust MPC, illustrating the method’s practical potential for networks such as power systems and microgrids.

Abstract

Adaptive model predictive control (MPC) robustly ensures safety while reducing uncertainty during operation. In this paper, a distributed version is proposed to deal with network systems featuring multiple agents and limited communication. To solve the problem in a distributed manner, structure is imposed on the control design ingredients without sacrificing performance. Decentralized and distributed adaptation schemes that allow for a reduction of the uncertainty online compatibly with the network topology are also proposed. The algorithm ensures robust constraint satisfaction, recursive feasibility and finite gain $\ell_2$ stability, and yields lower closed-loop cost compared to robust distributed MPC in simulations.

A distributed framework for linear adaptive MPC

TL;DR

This work tackles the scalability and decentralization challenges of adaptive MPC for interconnected networks by proposing a distributed adaptive MPC (DAMPC) framework. It imposes a structured optimization design and employs ADMM to solve the online MPC problem in a distributed fashion, while enabling online set-membership identification in both decentralized and distributed forms. The main contributions are (i) a linear-growth, distributed optimization formulation with block-diagonal costs and neighbor-constrained interactions, (ii) two identification schemes that tighten parameter bounds without a central unit, and (iii) guarantees of robust constraint satisfaction, recursive feasibility, and finite-gain stability, demonstrated on an uncertain mass-spring-damper network. The results show that adapting parameters via distributed identification yields meaningful cost reductions compared to a non-adaptive distributed robust MPC, illustrating the method’s practical potential for networks such as power systems and microgrids.

Abstract

Adaptive model predictive control (MPC) robustly ensures safety while reducing uncertainty during operation. In this paper, a distributed version is proposed to deal with network systems featuring multiple agents and limited communication. To solve the problem in a distributed manner, structure is imposed on the control design ingredients without sacrificing performance. Decentralized and distributed adaptation schemes that allow for a reduction of the uncertainty online compatibly with the network topology are also proposed. The algorithm ensures robust constraint satisfaction, recursive feasibility and finite gain stability, and yields lower closed-loop cost compared to robust distributed MPC in simulations.

Paper Structure

This paper contains 8 sections, 1 theorem, 23 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Adaptive MPC
  3. Distributed adaptive MPC
  4. Structured design matrices
  5. Set membership identification
  6. Distributed optimization
  7. Illustrative example
  8. Conclusions

Key Result

Proposition 1

The DAMPC algorithm guarantees robust constraint satisfaction and recursive feasibility of the optimization problem. In addition, the closed loop defined by the system eq:Dynamics and the DAMPC scheme is finite gain $\ell_2$ stable.

Figures (3)

  • Figure 1: Example interconnected network. The parameters affecting each agent are reported below.
  • Figure 2: Mass-spring-damper interconnected system.
  • Figure 3: Parameter bounds obtained from decentralized and distributed identification techniques. On the left, estimates of each agent are indicated in the legend. On the right, shared estimates are shown in purple.

Theorems & Definitions (1)

  • Proposition 1