Distributed adaptive barrier function-based integral sliding mode consensus control of multi-agent systems

This paper addresses the design of distributed adaptive control protocols for leader-follower consensus and time-varying formation problems, where agents communicate over directed graphs. Projection operator-based adaptive control protocols are developed for multi-agent systems modelled as general uncertain linear dynamics. An integral sliding mode-based robust control strategy is developed to compensate for the unknown bounded disturbance in the followers' dynamics. To relax the knowledge of the upper bound of the disturbance in designing a sliding-mode controller, a barrier function-based adaptive integral sliding-mode controller is designed to adjust the gain of the discontinuous part of the controller. This technique avoids overestimation of gains, which significantly reduces chattering. This control technique ensures the convergence of disagreement variables in a predefined neighborhood of zero. The Lyapunov-based stability proof demonstrates the convergence of disagreement variables in leader-follower consensus and time-varying formation control problems. Finally, numerical examples are provided to validate the efficacy of the proposed protocols.