Observer-based adaptive fault-tolerant event-triggered consensus for linear multiagent systems: a chattering-free approach

This paper investigates the distributed observer-based adaptive event-triggered consensus problem for linear multiagent systems (MASs) with time-varying multiplicative faults and bounded matched uncertainties. The presence of time-varying faults and non-identical uncertainties imposes significant challenges to achieving robust event-triggered consensus. To address these challenges, we propose a distributed observer-based continuous adaptive fault-tolerant event-triggered protocol that inherently eliminates the chattering. This protocol mitigates the impacts of uncertainties by introducing a nonlinear term with a time-varying boundary layer width. Then, to ensure fault tolerance, a real-time fault estimation (FE) mechanism is co-designed with adaptive coupling gain to accurately estimate unknown time-varying multiplicative faults. By incorporating these estimates, an adaptive event-based relative observer achieves precise state estimation without requiring direct transmission of actual states. Furthermore, the adaptive coupling gain is combined with online FE to actively enhance the robustness of the control law and event-triggering conditions, eliminating dependence on global communication graph parameters. Using Lyapunov-based analysis, we demonstrate that this protocol guarantees asymptotic consensus and rules out Zeno behaviour. In addition, an adaptive dynamic event-triggering mechanism (ADETM) avoids continuous communication for both control updates and event detection, thereby reducing the number of event triggers while ensuring efficient communication. A simulation example demonstrates the effectiveness of the proposed approach.