Fixed-Time Containment Tracking Control of Fractional-Order Multi-Vehicle Systems with Multiple Leaders: SMC approach

This paper addresses sliding mode control (SMC) design for disturbed fractional-order multi-vehicle networks in order to achieve containment tracking within a certain settling time. The multi-leader case is investigated where the aim of the containment protocol design is that the states of the fractional-order followers eventually are placed inside a convex hull made by the states of the leaders. The convergence rate is designed such that achieving the containment tracking occurs in a fixed-time manner. Unlike the previous works on finite-time containment control protocols of multi-agent systems, here, we offer a tractable design as the upper limit of the settling time of the convergence is achieved independent of the preliminary conditions of the vehicles' states. A novel SMC approach is proposed which enables the multi-vehicle network to reach the containment tracking at presence of the external disturbances. The numerical simulations reveal the correctness and effectiveness of the proposed theoretical approaches.