Robust Adaptive Cooperative Control for Formation-Tracking Problem in a Network of Non-Affine Nonlinear Agents

Abstract

In this chapter, a decentralized cooperative control protocol is proposed with application to any network of agents with non-affine nonlinear multi-input-multi-output (MIMO) dynamics. Here, the main purpose of cooperative control protocol is to track a time-variant reference trajectory while maintaining a desired formation. The reference trajectory is defined to a leader, which has at least one information connection with one of the agents in the network. The design procedure includes a robust adaptive law for estimating the unknown nonlinear terms of each agent's dynamics in a model-free format, that is, without the use of any regressors. Moreover, an observer is designed to have an approximation on the values of control parameters for the leader at the agents without connection to the leader. The entire design procedure is analysed successfully for the stability using Lyapunov stability theorem. Finally, the simulation results for the application of the proposed method on a network of nonholonomic wheeled mobile robots (WMR) are presented. Desirable leader-following tracking and geometric formation control performance have been successfully demonstrated through simulated group of wheeled mobile robots.

Optimal model‐free control for a generic MIMO nonlinear system with application to autonomous mobile robots

“…The mathematical model for kinematics and dynamics of a WMR (Figure 8) can be considered as follows 34 :…”

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

“…A robust adaptive cooperative control is proposed by Mahyuddin and Safaei 26 for formation-tracking problem, whereby the system matrix for dynamic system is assumed to be known. In this article, however, the system matrix is completely unknown and to be estimated with a model-free adaptive law.…”

“…In this article, however, the system matrix is completely unknown and to be estimated with a model-free adaptive law. In contrast to the previous work by Mahyuddin and Safaei, 26 the main controller gains are, instead, determined online. Another salient feature exemplified in this article is that the proposed cooperative controller considers an optimal policy by virtue of RL to find a solution to the algebraic Riccati equation.…”