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

Abstract

This paper proposes a data-driven approach to designing adaptive suboptimal second-order sliding mode (ASSOSM) controllers for a class of single-input nonlinear systems with partially unknown dynamics, subject to both matched and unmatched disturbances. We first view the system as comprising two coupled dynamics, referred to as the upper and lower dynamics, with the last state serving as a virtual input to the upper dynamics. The proposed control-design methodology then follows a two-stage procedure: (i) designing a virtual state-feedback control law for the upper dynamics and (ii) synthesizing an ASSOSM controller for the full-order system. To this end, we collect noise-corrupted data from the system throughout a finite-time experiment. We then formulate a data-dependent condition, whose feasibility enables the design of a virtual state-feedback control law that renders the closed-loop upper dynamics input-to-state stable with respect to the unmatched disturbance. Building on this virtual state-feedback control law, we subsequently propose a data-driven nonlinear sliding variable, based on which an ASSOSM controller is designed for the full-order system. The state trajectories of the resulting closed-loop system are semiglobally ultimately bounded (S-GUB), with the ultimate bound explicitly depending on the magnitude of the unmatched disturbance. In particular, the control design parameters can be selected for any prescribed bounded set of initial conditions so that the state trajectories of the closed-loop system are S-GUB. Moreover, the effect of the matched disturbance is totally rejected after a finite time. The effectiveness of the proposed method is satisfactorily demonstrated in the simulation.