Distributed optimization of nonlinear uncertain systems: An adaptive backstepping design

This paper proposes a Lyapunov-based adaptive backstepping approach to distributed optimization of nonlinear uncertain multi-agent systems. The model of each agent is in the strict-feedback form with parametric uncertainties. By only using local objective functions, this paper aims to solve the distributed optimization problem for the multi-agent system such that the outputs of the agents converge to the optimizer of the total objective function. Based on the idea of adaptive backstepping, the distributed optimization problem for the high-order multi-agent system is decomposed into solving the optimization or control problem for multiple first-order subsystems. The technical contributions lie in a Lyapunov-based design for distributed optimization, and a refined nonlinear damping design to deal with the newly appearing nonlinear uncertain terms caused by optimization. Based on the new designs, a Lyapunov function is constructed for the entire system, and the LaSalle-Yoshizawa Theorem is employed for convergence analysis. It is shown that the objective of distributed optimization is achievable if the local objective functions are convex with at least one of them being strongly convex. Computer-based numerical simulation is employed to show the effectiveness of the proposed design.