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Robust output synchronization of a network of heterogeneous nonlinear agents via nonlinear regulation theory

In this paper, we consider the output synchronization problem for a network of heterogeneous diffusively-coupled nonlinear agents. Specifically, we show how the (non-identical) agents can be controlled in such a way that their outputs asymptotically track the output of a prescribed nonlinear exosystem. The problem is solved in two steps. In the first step, the problem of achieving consensus among (identical) nonlinear reference generators is addressed. In this respect, it is shown how the techniques recently developed to solve the consensus problem among linear agents can be extended to agents modeled by nonlinear d-dimensional differential equations, under the assumption that the communication graph is connected. In the second step, the theory of nonlinear output regulation is applied in a decentralized control mode, to force the output of each agent of the network to robustly track the (synchronized) output of a local reference model.