Global asymptotic practical stability of perturbation-based extremum-seeking control for complex nonlinear systems...

This paper investigates the extremum-seeking control problem for complex nonlinear systems, aiming to regulate the system output toward a fixed value that maximizes an unknown nonlinear mapping under relaxed conditions. To address this challenge, a novel hierarchical framework is introduced, which decomposes the closed-loop system and reformulates the problem as a stability analysis of an interconnected system. Distinct from conventional methods that rely on exponential stability of the boundary-layer system, the proposed framework ensures robust stability against bounded disturbances by exploiting interconnected gain relations among hierarchical subsystems, while the nonlinear small-gain theorem is employed to ensure the overall stability and feasibility of the proposed approach. Compared to existing literatures, the proposed design allows the global extremum-seeking problem in uncertain nonlinear systems to be solved under more relaxed conditions. Finally, numerical simulations on various nonlinear systems demonstrate the effectiveness and practical applicability of the theoretical results.