Leader-Based Optimal Coordination Control for the Consensus Problem of Multiagent Differential Games via Fuzzy Adaptive Dynamic Programming

TL;DR

This paper introduces a novel fuzzy adaptive dynamic programming approach using generalized fuzzy hyperbolic models to design optimal coordination controls for multi-agent consensus problems, improving efficiency and stability.

Contribution

It pioneers the use of GFHMs for solving coupled Hamilton-Jacobi equations in multi-agent differential games with a single-network architecture.

Findings

The scheme achieves stable, cooperative multi-agent consensus.

The approach effectively approximates value functions of coupled HJ equations.

The control and estimation errors are proven to be bounded.

Abstract

In this paper, a new on-line scheme is presented to design the optimal coordination control for the consensus problem of multi-agent differential games by fuzzy adaptive dynamic programming (FADP), which brings together game theory, generalized fuzzy hyperbolic model (GFHM) and adaptive dynamic programming. In general, the optimal coordination control for multi-agent differential games is the solution of the coupled Hamilton-Jacobi (HJ) equations. Here, for the first time, GFHMs are used to approximate the solution (value functions) of the coupled HJ equations, based on policy iteration (PI) algorithm. Namely, for each agent, GFHM is used to capture the mapping between the local consensus error and local value function. Since our scheme uses the single-network rchitecture for each agent (which eliminates the action network model compared with dual-network architecture), it is a more reasonable architecture for multi-agent systems. Furthermore, the approximation solution is utilized to obtain the optimal coordination controls. Finally, we give the stability analysis for our scheme, and prove the weight estimation error and the local consensus error are uniformly ultimately bounded. Further, the control node trajectory is proven to be cooperative uniformly ultimately bounded.