Fault-Tolerant Formation Control for Stochastic Multi-Agent Systems with Noise and Channel Interference

This paper investigates the fault-tolerant (FT) formation control problem with guaranteed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance for multiagent systems (MASs) in the presence of actuator faults. The authors consider a realistic scenario where communication between adjacent agents is subject to disturbances, and each agent is affected by stochastic disturbances and measurement noise. For each agent, a decentralized state observer and an adaptive fault estimator are designed. Based on these, a novel cooperative fault-tolerant formation control (FTFC) strategy is proposed to ensure that all agents achieve the desired formation. Considering the influence of system noise, the error dynamics are modeled using Itô stochastic differential equations, providing a foundation for the design and analysis of the Lyapunov function within the Itô calculus framework. It is demonstrated that the proposed FTFC scheme ensures mean-square asymptotic stability of the formation error system with a specified <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> attenuation level. The observer, estimator, and controller gains are computed by solving algebraic Riccati inequalities.