Quantum mechanics

Hamilton–Jacobi–Bellman equation

Control (management)

Affine transformation

Pure mathematics

Multi-agent system

Theoretical computer science

Computer science

Mathematical optimization

Distributed computing

Physics

Nonlinear system

Reinforcement learning

Fault tolerance

Graph

Mathematics

Artificial intelligence

Optimal control

Combinatorics

Topology (electrical circuits)

Control theory (sociology)

Journal of the Franklin Institute

The goal of this paper is to propose an optimal fault tolerant control (FTC) approach for multi-agent systems (MASs). It is assumed that the agents have identical affine dynamics. The underlying communication topology is assumed to be a directed graph. The concepts of both inverse optimality and partial stability are further employed for designing the control law fully developed in the paper. Firstly, the optimal FTC problem for linear MASs is formulated and then it is extended to MASs with affine nonlinear dynamics. To solve the Hamilton-Jacobi-Bellman (HJB) equation, an Off-policy Reinforcement Learning is used to learn the optimal control law for each agent. Finally, a couple of numerical examples are provided to demonstrate the effectiveness of the proposed scheme.

Fault tolerant cooperative control for affine multi-agent systems: An optimal control approach