  In this note, a novel observer-based output feedback control approach is
proposed to address the distributed optimal output consensus problem of
uncertain nonlinear multi-agent systems in the normal form over unbalanced
directed graphs. The main challenges of the concerned problem lie in unbalanced
directed graphs and nonlinearities of multi-agent systems with their agent
states not available for feedback control. Based on a two-layer controller
structure, a distributed optimal coordinator is first designed to convert the
considered problem into a reference-tracking problem. Then a decentralized
output feedback controller is developed to stabilize the resulting augmented
system. A high-gain observer is exploited in controller design to estimate the
agent states in the presence of uncertainties and disturbances so that the
proposed controller relies only on agent outputs. The semi-global convergence
of the agent outputs toward the optimal solution that minimizes the sum of all
local cost functions is proved under standard assumptions. A key feature of the
obtained results is that the nonlinear agents under consideration are only
required to be locally Lipschitz and possess globally asymptotically stable and
locally exponentially stable zero dynamics.

Systems and Control;Systems and Control;Optimization and Control