Global Bipartite Output Consensus of Discrete-Time Heterogeneous Linear Systems Subject to Input Saturation: A Model-Free Approach

Abstract

In this article, we propose a model-free approach for solving the bipartite output consensus problem of discrete-time heterogeneous multiagent systems subject to input saturation over a weighted directed network. We propose both a distributed reference generator and a control law based on the low-gain approach for each follower agent in the system. We show that all the control laws together achieve semiglobal bipartite output consensus. Furthermore, we present a Q-learning algorithm to obtain both the low-gain parameter and the feedback gain matrix in the control law. We also present an online output-tracking-error-based updating algorithm to obtain the feedforward gain matrix in the control law. Thus, these control laws no more rely on the dynamics of linear systems. We show that the input saturation during the online updating algorithm does not affect the convergence of the algorithm. The control laws calculated from the model-free algorithms can prevent input saturation from occurring, and thus, the heterogeneous multiagent systems achieve global bipartite output consensus. Finally, we provide a numerical example for validating the theoretical results.