Hamilton–Jacobi–Bellman equation

Scheme (mathematics)

Multi-agent system

Theoretical computer science

Bipartite graph

Computer science

Mathematical optimization

Reinforcement learning

Graph

Mathematics

Mathematical analysis

Artificial intelligence

Optimal control

Artificial neural network

Applied Mathematics and Computation

In this paper, the optimal bipartite consensus control (OBCC) problem is investigated for unknown multi-agent systems (MASs) with coopetition networks. A novel distributed OBCC scheme is proposed based on model-free reinforcement learning method to achieve OBCC, where the agent’s dynamics are no longer required. First, The coopetition networks are applied to establish the cooperative and competitive interactions among agents, and then the OBCC problem is formulated by introducing local neighbor bipartite consensus errors and performance index functions (PIFs) for each agent. Second, in order to obtain the OBCC laws, a policy iteration algorithm (PIA) is employed to learn the solutions to discrete-time (DT) Hamilton-Jacobi-Bellman (HJB) equations. Third, to implement the proposed methods, we adopt a data-driven actor-critic-based neural networks (NNs) framework to approximate the control laws and the PIFs, respectively, in an online learning manner. Finally, some simulation results are given to demonstrate the effectiveness of the developed approaches.

A novel optimal bipartite consensus control scheme for unknown multi-agent systems via model-free reinforcement learning