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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.

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.

In this paper, we consider Linear Quadratic (LQ) control problem with process and measurement noises. We analyze the LQ problem in terms of the average cost and the structure of the value function. We assume that the dynamics of the linear system is unknown and only noisy measurements of the state variable are available. Using noisy measurements of the state variable, we propose two model-free iterative algorithms to solve the LQ problem. The proposed algorithms are variants of policy iteration routine where the policy is greedy with respect to the average of all previous iterations. We rigorously analyze the properties of the proposed algorithms, including stability of the generated controllers and convergence. We analyze the effect of measurement noise on the performance of the proposed algorithms, the classical off-policy, and the classical Q-learning routines. We also propose a model-building approach where a model of the dynamical system is estimated and the optimal control problem is solved assuming that the estimated model is the true model. We use a benchmark to evaluate and compare our proposed algorithms with the classical off-policy, the classical Q-learning, and the policy gradient. We show that our model-building approach performs nearly identical to the analytical solution and our proposed policy iterationbased algorithms outperform the classical off-policy and the classical Q-learning algorithms on this benchmark but do not outperform the model-building approach.

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