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In this note, a novel observer-based output feedback control approach isproposed to address the distributed optimal output consensus problem ofuncertain nonlinear multi-agent systems in the normal form over unbalanceddirected graphs. The main challenges of the concerned problem lie in unbalanceddirected graphs and nonlinearities of multi-agent systems with their agentstates not available for feedback control. Based on a two-layer controllerstructure, a distributed optimal coordinator is first designed to convert theconsidered problem into a reference-tracking problem. Then a decentralizedoutput feedback controller is developed to stabilize the resulting augmentedsystem. A high-gain observer is exploited in controller design to estimate theagent states in the presence of uncertainties and disturbances so that theproposed controller relies only on agent outputs. The semi-global convergenceof the agent outputs toward the optimal solution that minimizes the sum of alllocal cost functions is proved under standard assumptions. A key feature of theobtained results is that the nonlinear agents under consideration are onlyrequired to be locally Lipschitz and possess globally asymptotically stable andlocally exponentially stable zero dynamics.

Distributed Optimal Output Consensus of Uncertain Nonlinear Multi-Agent Systems over Unbalanced Directed Networks via Output Feedback