Distributed Feedback Optimization of Nonlinear Uncertain Systems Subject to Inequality Constraints

This article studies the distributed feedback optimization problem for nonlinear uncertain multi-agent systems subject to inequality constraints. A new class of distributed optimization algorithms is proposed by extending the standard primal-dual dynamics and introducing two new inputs to deal with the couplings arising from feedback optimization. With each controlled agent satisfying a mild dissipation assumption, the proposed distributed feedback optimization algorithms, using only the output-dependent gradient value of each agent's corresponding local objective function and the information from its neighboring agents, can steer the outputs of the agents to a common set-point, which minimizes the total objective function while satisfying the inequality constraints. A composite Lyapunov function is constructed to prove global asymptotic stability of the closed-loop system at the equilibrium corresponding to the optimal point.