Fault-Tolerant Adaptive Synchronization for High-Order Discrete-Time Multiagent Systems With Stochastic Noises

This paper addresses fault-tolerant adaptive synchronization for a category of high-order discrete-time multi-agent systems (MASs) influenced by stochastic noise. Built upon a spanning directed acyclic graph (SDAG), a backstepping-based framework is introduced for implementing controllers. To be specific, under the proposed framework, all unknown information are accumulated at last step and only one neural network (NN) is utilized to implement the controller design for each agent. As a consequence, the corresponding intermediate NN approximations for virtual controllers are released. Furthermore, circular dependencies are avoided with the assistance of SDAG, ensuring the feasibility of the controllers in multiagent setting. By utilizing the Lyapunov difference approach, all signals in the MASs are guaranteed to be exponential mean-square (EMS) bounded. Ultimately, simulation studies involving five pendulum systems are performed to demonstrate the effectiveness of the proposed strategy. Note to Practitioners - In contemporary applications, MASs are increasingly prone to experiencing various faults, arising from both complex operational environments and intricate interactions among agents. Such faults, if not promptly identified and addressed, can severely compromise the performance and reliability of MAS-based applications. Additionally, MASs are typically characterized by inherent nonlinearity and operate under digital control, which imposes the significance to develop nonlinear discrete-time control strategies. Consequently, this article proposes novel adaptive NN control strategies for a type of high-order nonlinear MASs to achieve output synchronization. Furthermore, actuator faults and stochastic noises are considered. The proposed fault-tolerant control strategies integrate adaptive NN approximations and a compensation term for fault mitigation, ensuring that the synchronization errors converge to a neighborhood of the origin through proper parameter adaptation.