A robust damping-based sliding mode extremum seeking framework for perturbed strict-feedback nonlinear systems

Despite their attractive robustness properties, existing Sliding Mode Extremum Seeking (SMES) approaches remain susceptible to performance degradation in the presence of matched and, especially, unmatched perturbations. To overcome this limitation, this article proposes a novel SMES framework for perturbed strict-feedback nonlinear systems by integrating a damping-enhanced SMES scheme with a Backstepping-based Barrier Integral Sliding Mode Control (BBF-ISMC) strategy that adopts barrier functions through a unified formulation for direct integration with the SMES scheme. The proposed approach enables robust extremum-seeking performance with smooth control action and without the need for any prior knowledge of the bounds on perturbations. Practical finite-time stability is established for a small set around the extremum point via rigorous stability analysis. The approach is validated through a simulation-based comparative study on a UAV antenna tracking system.