Distributed Feedback Optimization of Networked Nonlinear Systems Using Relative Output Measurements*

This paper investigates the distributed feedback optimization problem of nonlinear multi-agent systems. In such systems, each agent can measure the relative outputs between itself and its neighbors but lacks access to their absolute states and internal controller states. By combining distributed optimization and singular perturbation methods, a novel distributed controller design is presented, that relies solely on each agent's real-time gradient values of its local objective function and its relative output measurements to neighboring agents. The boundedness of the closed-loop signals and the convergence of the agent outputs to the minimizer of the total cost are proved rigorously. A numerical example is conducted to validate the effectiveness of the proposed approach.