Distributed Model Predictive Control Design for Multi-agent Systems via Bayesian Optimization

TL;DR

This work tackles the challenge of designing distributed model predictive controllers (DMPC) for large-scale, interconnected multi-agent systems when local MPC models are imperfect. It couples DMPC with multi-agent Markov decision processes via a parameterized DMPC formulation and learns the DMPC parameters in a coordinated ADMM-based Bayesian optimization (MABO) framework, enabling improved closed-loop performance despite model mismatch. The authors provide formal arguments toward optimality and convergence, describe a Gaussian Process-based surrogate and an expected-improvement acquisition within a distributed optimization scheme, and validate the approach through numerical examples on linear multi-agent systems and a formation-control scenario. The proposed MABO-DMPC offers a data-efficient, scalable method to tune distributed controllers while respecting coupling constraints, with potential impact on robotics, energy networks, and other large-scale cyber-physical systems.

Abstract

This paper introduces a new approach that leverages Multi-agent Bayesian Optimization (MABO) to design Distributed Model Predictive Control (DMPC) schemes for multi-agent systems. The primary objective is to learn optimal DMPC schemes even when local model predictive controllers rely on imperfect local models. The proposed method invokes a dual decomposition-based distributed optimization framework, incorporating an Alternating Direction Method of Multipliers (ADMM)-based MABO algorithm to enable coordinated learning of parameterized DMPC schemes. This enhances the closed-loop performance of local controllers, despite discrepancies between their models and the actual multi-agent system dynamics. In addition to the newly proposed algorithms, this work also provides rigorous proofs establishing the optimality and convergence of the underlying learning method. Finally, numerical examples are given to demonstrate the efficacy of the proposed MABO-based learning approach.

Figures (10)

• Figure 1: An overview of the proposed MABO-based DMPC.
• Figure 2: The gray lines show the evolution of the actual distances during the learning process. The green lines show the desired distances between the first states of agents. The cyan lines show the evolution of the actual distances when a conventional DMPC without learning is used. The red lines show the evolution of the actual distances using a learned DMPC.
• Figure 3: The gray lines show the evolution of the first states during the learning process. For the first state of the agent $1$, we consider the point $0$ as reference and constraint simultaneously. The yellow region shows the unsafe zone. The cyan lines show the evolution of the first states when a conventional DMPC without learning is used. The red lines show the evolution of the first states using the proposed learned DMPC scheme.
• Figure 4: The gray lines show the evolution of control signals during the learning process. The cyan lines show the results when a conventional DMPC without learning is used while the red lines show the results obtained from using the learned DMPC.
• Figure 5: The evolution of the local closed-loop performance of agents during the learning process is shown comparing the proposed multi-agent BO (MABO) and conventional BO combined with DMPC.

Theorems & Definitions (17)

• Remark 1
• Remark 2
• Theorem 1
• proof
• Theorem 2
• proof
• Remark 3
• Corollary 1
• proof
• Proposition 1: BO as Finite-Horizon MDP