An Adaptive Continuous Approach to Consensus Tracking of Nonlinear Multiagent Systems With a Nonautonomous Leader

It is challenging and critical to achieve zero error consensus tracking in multiagent systems (MASs) with nonautonomous leaders (i.e., leaders with nonzero inputs). The traditional approach is to use discontinuous controllers which may cause a chattering phenomenon. How to achieve zero error consensus tracking via a chattering-free controller is still open. We propose a class of adaptive continuous controllers to achieve zero error consensus tracking for Lipschitz nonlinear MASs with a nonautonomous leader and directed communication topology. Unlike existing works that use discontinuous functions to eliminate the impacts of leaders' inputs, we use a continuous function by introducing an exponential decay function into the denominator. First, we design a continuous controller with fixed coupling strengths and prove that zero error consensus tracking can be achieved if the coupling strengths are greater than some positive constants. Second, we design a continuous controller with dynamic coupling strengths under which fully distributed zero error consensus tracking can be achieved. Moreover, the case with undirected communication topology is studied. Finally, three examples are given to verify the theoretical results. Specifically, convergence results between the continuous controller here and that is developed via the boundary layer technique are compared. Compared with existing works, the designed adaptive continuous controllers here can not only achieve zero error consensus tracking but also is chattering free.