Observer-Based Fault-Tolerant Boundary Consensus Control for Nonlinear Delayed PDE Multi-Agent Systems With Stochastic Actuator Failures

Abstract

This study investigates the observer-based fault-tolerant boundary consensus control problem for nonlinear delayed multi-agent systems (MASs) governed by partial differential equations (PDEs) with stochastic actuator faults. First, the nonlinear delayed PDE MASs subject to Markov jump actuator faults are modeled by explicitly accounting for the actuator failure modes. Then, based on a directed graph and boundary measurements, an observer-based fault-tolerant boundary consensus controller is developed, which reduces the implementation cost by using only boundary actuators and sensors. Sufficient conditions for ensuring exponential consensus are derived using inequality techniques and the Lyapunov direct method, and the consensus conditions are formulated as linear matrix inequalities (LMIs). Finally, numerical simulations are provided to demonstrate the validity of the proposed observer-based fault-tolerant boundary consensus control method. Note to Practitioners—Actuator faults and time delays are critical concerns in consensus control due to their frequent occurrence in practical MASs. These factors may lead to performance degradation. Existing consensus control strategies for nonlinear delayed PDE MASs typically rely on distributed actuation and sensing over the entire spatial domain, which results in high implementation costs and complex hardware requirements. Furthermore, most existing approaches assume deterministic actuator fault models and do not account for stochastic failures. To overcome these challenges, this paper proposes an observer-based fault-tolerant boundary consensus control method for nonlinear delayed PDE MASs subject to stochastic actuator faults. By utilizing only boundary actuators and sensors, the proposed scheme significantly reduces sensing and actuation requirements while maintaining robustness against stochastic fault occurrences. The controller design is transformed into a convex optimization problem via Lyapunov direct method and LMI techniques, facilitating numerical implementation. Numerical simulations are provided to demonstrate the effectiveness of the presented observer-based fault-tolerant boundary consensus control strategy.