Novel distributed event/self-triggered sliding-mode control: Application to practical fixed-time consensus of second-order multi-agent systems

This paper presents a novel terminal sliding-mode control (SMC) protocol to accomplish the practical fixed-time (PFXT) consensus of second-order multi-agent systems (MASs) through event-triggered scheme (ETS). The main challenge is the digitization of SMC which prevents the controlled system from reaching an ideal sliding phase and the singularity problem in terminal sliding-mode controllers. Firstly, a novel method of PFXT stability is proposed, which guarantees the non-singularity for the controller. Secondly, based on the proposed PFXT control method, a practical non-singular terminal SMC strategy is designed to accomplish the PFXT consensus of MASs through ETS. Besides, a strictly positive minimal triggering interval of each follower is given to exclude the Zeno phenomenon. Different with conventional terminal SMC, maintaining the sliding trajectory constrained on the sliding manifold is not a premise to guarantee the system stability. Then, to eliminate the requirement of continuous monitoring for ETS, the SMC strategy is generalised to the self-triggered approach. At last, a numerical example is presented to validate the developed methods.