Distributed adaptive model-free cooperative control for a network of generic unknown nonlinear systems

Abstract

In this article, a distributed model-free consensus control is proposed for a network of nonlinear agents with unknown nonlinear dynamics, unknown process disturbances, and white noise measurement disturbances. Here, the purpose of the control protocol is to first synchronize the states of all follower agents in the network to a leader and then track a reference trajectory in the state space. The leader has at least one information connection with one of the follower agents in the network. The design procedure includes adaptive laws for estimating the unknown linear and nonlinear terms of each agent’s dynamics. The salient feature of the proposed control scheme is that each agent’s estimation is a model-free adaptive law, that is, the need for regressor or linear-in-parameter basis is alleviated. In addition, without requiring direct connection to the leader, the leader’s control input can still be reconstructed by virtue of a robust observer which can be defined in a distributed manner in the network. The entire design procedure is analyzed successfully for the stability using Lyapunov stability theorem. In addition, it is shown that the proposed distributed controller includes an optimal term. Besides, a modified Kalman filter is added to eliminate the measurement noise. Finally, the simulation results on three networks of unknown nonlinear systems are presented. Moreover, a comparative study is presented to evaluate the proposed algorithm against a model-based cooperative control algorithm.