Prescribed-time leader-following consensus for stochastic second-order multi-agent systems subject to actuator failures via sliding mode control strategy

Abstract

Two control protocols based on the sliding mode control scheme are proposed to solve the prescribed-time leader-following consensus problem for second-order nonlinear multi-agent systems with actuator failures and stochastic noises under directed topology. First, a discontinuous controller protocol is proposed when the parameters related to the actuator failures can be acquired in advance. The controller can drive the system trajectories to reach the sliding manifold before a predefined time, and then ensure that the leader-following consensus is achieved in predefined time also. The upper bound of the reaching time and the upper bound of the setting time do not depend on initial conditions and system parameters, and can be arbitrarily specified offline. Next, when the prior knowledge of the actuator faults and nonlinearities cannot be obtained, a continuous control protocol is proposed, which can adaptively adjust the control gains to compensate for these unknown uncertainties. We theoretically prove that the prescribed-time leader-following consensus in mean square can be achieved under the designed control schemes. Finally, several examples are presented to illustrate the effectiveness of the proposed solutions.