Sliding Mode Control for Stochastic Systems: A little Fantasy and Discussion

The convencional Sliding Mode Control (SMC) theory has been developed for the control design of deterministic systems containing a bounded matched uncertainties. The case when a model is governed by the Ito's stochastic differential equation, containing unbounded stochastic (usually, Gaussian) "white noise", has not been studied up to now. In this presentation we discuss some possible situations arising in stochastic SMC systems and show that SMC controllers preserve their properties in a special sense: almost all trajectories leave a bounded region around origin a finite number of times.