Robust adaptive fault-tolerant consensus control for uncertain nonlinear fractional-order multi-agent systems with directed topologies

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This paper investigates the problem of fault-tolerant consensus control (FTCC) for heterogeneous nonlinear fractional-order multi-agent systems with general directed topology, where the systems are subject to heterogeneous unknown and time-varying inertias, coupling nonlinearities, external disturbances, and actuator failures. A continuous robust adaptive FTCC protocol is designed by using a boundary layer technique to compensate for the time-varying unknown inertias, uncertain coupling dynamics/disturbances, and unpredictable actuation failures simultaneously. By artfully choosing a Lyapunov function and by generalizing an important fractional-order inequality, it is shown that the consensus configuration error converges to an adjustable small residual set in finite time. The proposed robust adaptive FTCC protocol is completely distributed in the sense that there is no need for any global information, and also is less demanding without requiring any detailed dynamic/parameters information or complicated/costly fault detection and diagnosis. The effectiveness of the proposed FTCC scheme is illustrated by numerical simulation.