Distributed Average Tracking for Lipschitz-Type Nonlinear Dynamical Systems

TL;DR

This paper develops three distributed algorithms for average tracking in Lipschitz-type nonlinear systems, addressing robustness, adaptivity, and implementation ease, enabling agents to track reference signals effectively.

Contribution

It introduces novel distributed algorithms that handle nonlinear Lipschitz conditions, including robust, adaptive, and continuous versions, enhancing tracking performance and practicality.

Findings

Robust algorithm works without identical initial conditions.

Adaptive algorithm removes the need to know the Lipschitz constant.

Continuous algorithm reduces chattering and improves implementation.

Abstract

In this paper, a distributed average tracking problem is studied for Lipschitz-type nonlinear dynamical systems. The objective is to design distributed average tracking algorithms for locally interactive agents to track the average of multiple reference signals. Here, in both the agents' and the reference signals' dynamics, there is a nonlinear term satisfying the Lipschitz-type condition. Three types of distributed average tracking algorithms are designed. First, based on state-dependent-gain designing approaches, a robust distributed average tracking algorithm is developed to solve distributed average tracking problems without requiring the same initial condition. Second, by using a gain adaption scheme, an adaptive distributed average tracking algorithm is proposed in this paper to remove the requirement that the Lipschitz constant is known for agents. Third, to reduce chattering and make the algorithms easier to implement, a continuous distributed average tracking algorithm based on a time-varying boundary layer is further designed as a continuous approximation of the previous discontinuous distributed average tracking algorithms.