Data-Driven Adaptive Second-Order Sliding Mode Control with Noisy Data

Abstract: This paper offers a data-driven approach for designing adaptive suboptimal second-order sliding mode (ASSOSM) controllers for single-input nonlinear systems, characterized by perturbed strict-feedback structures with unknown dynamics. The proposed approach is recursive, in which the system dynamics are first decomposed into two parts, referred to as the upper and lower dynamics. The control design task is then divided into two stages, that is, designing a virtual controller for the upper dynamics, followed by synthesizing the actual controller for the full-order system. To this end, we start by collecting noisy data from the system through a finite-time experiment, referred to as a single trajectory. We then formulate a data-dependent condition as a semidefinite program, whose feasibility enables the design of a virtual controller that ensures global asymptotic stability of the origin for the upper dynamics. Building upon this virtual controller, we subsequently propose a data-driven sliding variable that facilitates the design of an ASSOSM controller for the unknown full-order system. This controller guarantees semi-global asymptotic stability of the origin in the presence of disturbances. Specifically, for any prescribed bounded set--no matter how large--the controller's design parameters can be chosen to ensure asymptotic stability of the origin. The effectiveness of the proposed method is demonstrated through three case studies, reflecting different aspects of the approach.