Adaptive Tracking for Stochastic Nonlinear Systems With Markovian Switching $ $

The problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary Markovian switching is considered in this note. An Ito formula is proposed for stochastic integral equations with an integral about martingale measure. An adaptive backstepping controller is designed such that the closed-loop system has a unique solution that is globally bounded in probability and
L
₄
-norm of the tracking error converges to an arbitrarily small neighborhood of zero. A simulation example demonstrates the efficiency of the proposed scheme.