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.
In this paper, we propose a delay independent control scheme that regulates to zero the state and the control input of a linear input delayed system whose open loop poles are at the origin. Two main features of our control scheme are its non-distributed nature in the sense that only the current state is used in the feedback, and its delay independence in the sense that no knowledge of the delay is required. The main ingredients of our control scheme and the regulation proof include a design of the delay independent truncated predictor feedback law with a time-varying feedback parameter, a Lyapunov function based adaptation of the time-varying parameter, a mechanism for switching between two update laws of the time-varying parameter, and the partial differential equation based analysis for delayed systems.
Stability and Control of Uncertain Systems
Stability and Controllability of Differential Equations