Cooperative Output Regulation of Heterogeneous Unknown Systems via Passification-Based Adaptation

While several robust cooperative output regulation approaches for heterogeneous systems have been proposed (with fixed-gain distributed controllers), the design of adaptive-gain distributed controllers becomes relevant in dealing with larger uncertainty than robust approaches. This letter addresses the adaptive cooperative output regulation problem for heterogeneous systems with unknown linear dynamics, where possibly large system uncertainty would make fixed-gain robust approaches not applicable. A passification method is adopted to design adaptive-gain distributed controllers solving the problem. The proposed method includes two steps: in the first step, a distributed observer of the exogenous signal is designed for those systems that cannot access the exosystem, and a reference model is designed whose output can converge to the exogenous signal; in the second step, command generator tracking is achieved via adaptive laws that make the output of each system converge to the output of the reference model, and thus to the exogenous signal. Stability analysis is provided via a Lyapunov approach, and a numerical example illustrates the effectiveness of the approach.