Distributed Average Tracking for Lipschitz-Type of Nonlinear Dynamical Systems

In this paper, a distributed average tracking (DAT) problem is studied for Lipschitz-type of nonlinear dynamical systems. The objective is to design DAT algorithms for locally interactive agents to track the average of multiple reference signals. Here, in both dynamics of agents and reference signals, there is a nonlinear term satisfying a Lipschitz-type condition. Three types of DAT algorithms are designed. First, based on state-dependent-gain design principles, a robust DAT algorithm is developed for solving DAT problems without requiring the same initial condition. Second, by using a gain adaption scheme, an adaptive DAT algorithm is designed to remove the requirement that global information, such as the eigenvalue of the Laplacian and the Lipschitz constant, is known to all agents. Third, to reduce chattering and make the algorithms easier to implement, a couple of continuous DAT algorithms based on time-varying or time-invariant boundary layers are designed, respectively, as a continuous approximation of the aforementioned discontinuous DAT algorithms. Finally, some simulation examples are presented to verify the proposed DAT algorithms.