Modular design of adaptive robust controller for strict-feedback stochastic nonlinear systems

Abstract

A modular approach of the estimation-based design in adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noises and constant unknown parameters. By using Itô s differentiation rule, nonlinear damping and adaptive Backstepping procedure, the input-to-state stable controller of global stabilization in probability is developed, which guarantees that system states are bounded and the system has a robust stabilization. According to Swapping technique, we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed. Transient performance of the system is estimated by the norm of error. Results of simulation show the effectiveness of the control algorithms. The modular design, which has a concise hierarchy, is more flexible and versatile than a Lyapunov-based algorithm.

Keywords

Wiener noises, It / Arial" / >& / ocirc / ’s differentiation rule, Stabilization in probability, Input-to-state stability, Swapping technique