Reduced-order observer-based backstepping tracking control for a class of stochastic nonlinear systems

In this paper, an output feedback tracking control scheme is put forwarded for a class of stochastic nonlinear systems, whose dynamics involve not only unknown parameters but also unmeasured states multiplied by output nonlinearities. A type of reduced-order observer is first developed. By adding some output related items in the observer, the estimation error realize global asymptotic convergence under disturbance free condition, and global bounded convergence when considering disturbance. Besides, the dimension of the closed-loop system is reduced, and the update law of this observer gain is beneficial for steady tracking. After the observer was established, the controller is constructed by employing the adaptive backstepping approach, and a smooth nonsingular robust item is proposed to handle the influence of stochastic disturbance. All the signals in the closed system is proved to be globally bounded in probability. Moreover the output tracking error converges to an arbitrary small neighborhood of the origin by proper choosing of the design parameters. The simulation results based on current control scheme and the comparison with the previous method illustrate that the proposed output feedback scheme realizes good tracking performance and strong ability on stochastic disturbance attenuation.