Adaptive Integral Super-Twisting Sliding Mode Control for Uncertain Stochastic Systems

In this paper, we consider the adaptive integral super-twisting sliding mode control problem for stochastic systems with bounded uncertainties and state-multiplicative stochastic (Brownian) noise. We first introduce an integral-type sliding surface. Then, we develop the adaptive super-twisting controller which guarantees the reachability to the specified sliding surface in finite time. We also characterize a sufficient condition for stochastic stability of sliding motion in terms of a linear matrix inequality. Hence, the proposed controller first guarantees the finite-time convergence to the sliding surface and then achieves the stochastic stability of the closed-loop system in the predefined sliding surface under bounded uncertainties. Two simulation results are presented to illustrate the theoretical results and the effectiveness of the proposed control method.