Adaptive tracking control for stochastic nonlinear systems with unknown virtual control coefficients

This article studies the adaptive tracking control problem for stochastic nonlinear systems with unknown virtual control coefficients (UVCCs) being functions of system states. Without using the Nussbaum gain technique (NGT), a new method is introduced to deal with UVCCs. The novel adaptive laws are constructed to compensate parameter uncertainties and UVCCs. Using backstepping method, an adaptive controller is designed, which can ensure that the boundedness in probability of all the signals in the closed-loop system. In the end, a numerical simulation example and a practical example are given to validate the effectiveness and superiority of the proposed controller.