Distributed Experiment Design and Control for Multi-agent Systems with Gaussian Processes

TL;DR

This paper presents a distributed control framework for multi-agent systems using Gaussian Processes, combining experiment design and coordination via a novel ADMM-C algorithm, with proven convergence and demonstrated effectiveness.

Contribution

It introduces a new distributed optimization algorithm, ADMM-C, for efficient experiment design and control in multi-agent systems modeled by Gaussian Processes.

Findings

The ADMM-C algorithm converges to a stationary point under certain conditions.

The proposed method improves computational efficiency through distributed processing and convex optimization.

Numerical simulations validate the effectiveness of the approach in multi-vehicle formation control.

Abstract

This paper focuses on distributed learning-based control of decentralized multi-agent systems where the agents' dynamics are modeled by Gaussian Processes (GPs). Two fundamental problems are considered: the optimal design of experiment for concurrent learning of the agents' GP models, and the distributed coordination given the learned models. Using a Distributed Model Predictive Control (DMPC) approach, the two problems are formulated as distributed optimization problems, where each agent's sub-problem includes both local and shared objectives and constraints. To solve the resulting complex and non-convex DMPC problems efficiently, we develop an algorithm called Alternating Direction Method of Multipliers with Convexification (ADMM-C) that combines a distributed ADMM algorithm and a Sequential Convexification method. The computational efficiency of our proposed method comes from the facts that the computation for solving the DMPC problem is distributed to all agents and that efficient convex optimization solvers are used at the agents for solving the convexified sub-problems. We also prove that, under some technical assumptions, the ADMM-C algorithm converges to a stationary point of the penalized optimization problem. The effectiveness of our approach is demonstrated in numerical simulations of a multi-vehicle formation control example.