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Summary This paper addresses output regulation of heterogeneous linear multi‐agent systems. We first show that output regulation can be achieved through local controller design, then we formulate output regulation in the graphical game framework. To solve output regulation of heterogeneous linear multi‐agent system in the graphical game framework, one needs to derive a solution to the coupled Hamilton–Jacobi equations. Both offline and online algorithms are suggested for that solution. Using the online method, the profile policy converges to a Nash Equilibrium. Besides, it is shown that the graphical formulation is robust to the multiplicative uncertainty satisfying an upper bound and it has an infinite gain margin. Copyright © 2015 John Wiley & Sons, Ltd.

This paper investigates cooperative output synchronization and bipartite output synchronization of a group of linear heterogeneous agents in a unified framework. For a structurally balanced signed graph, we prove that the bipartite output synchronization is equivalent to the cooperative output synchronization over an unsigned graph whose adjacency matrix is obtained by taking the absolute value of each entry in the adjacency matrix of the signed graph. We obtain a new H∞-criterion which is sufficient for both cooperative output synchronization and bipartite output synchronization.

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In this paper, we introduce an optimal average cost learning framework to solve output regulation problem for linear systems with unknown dynamics. Our optimal framework aims to design the controller to achieve output tracking and disturbance rejection while minimizing the average cost. We derive the Hamilton-Jacobi-Bellman (HJB) equation for the optimal average cost problem and develop a reinforcement algorithm to solve it. Our proposed algorithm is an off-policy routine which learns the optimal average cost solution completely model-free. We rigorously analyze the convergence of the proposed algorithm. Compared to previous approaches for optimal tracking controller design, we elevate the need for judicious selection of the discounting factor and the proposed algorithm can be implemented completely model-free. We support our theoretical results with a simulation example.

In this paper we investigate bipartite output synchronization of a group of linear heterogeneous agents communicating their outputs over a signed graph. Our multiagent system contains N followers and one leader and we aim to achieve bipartite output synchronization to the output of the leader. By the bipartite output synchronization, we mean output synchronization in the modulus; while the modulus is the same for all the agents, the signs could be different. Assuming that the communication graph is structurally balanced, we show that the bipartite output synchronization over the signed graph is equivalent to the classical output synchronization over an unsigned graph whose adjacency matrix is the element-wise absolute value of the adjacency matrix of the signed graph. We propose explicit output-feedback controller in this paper and illustrate our theoretical development by a simulation example.

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