Adaptive Tracking Control for Random High-Order Fully Actuated Systems with Unknown Drift Nonlinearity and Diffusion Coefficient

This paper extends the high-order fully actuated system (HOFAS) theory to the adaptive tracking control of random nonlinear systems disturbed by second-order moment process. Firstly, a random high-order fully actuated system (RHOFAS) with unknown drift nonlinearity and diffusion coefficient is proposed. Secondly, an adaptive tracking controller is designed for this RHOFAS by virtue of the HOFAS theory and a radical basis function neural network (RBFNN). It is proved that the resulting closed-loop system is exponentially noise-to-state practically stable in mean square, the mean square of tracking error can converge to an arbitrarily small neighborhood of zero, and all signals in the closed-loop system is bounded in mean square. Finally, two simulation examples are provided to demonstrate the effectiveness of our proposed controller.