Output tracking of stochastic high‐order nonlinear systems perturbed by second‐order moment process

Abstract

In this paper, we study the output tracking problem of stochastic high‐order nonlinear systems perturbed by second‐order moment process. Unlike the existing results that focused on systems with wiener process, we consider a more practical noise, the second‐order moment process in this paper. We propose a new design method where piecewise functions are suitably constructed to deal with coupling terms between nonlinear functions and the noise. The designed controller ensures that the tracking error can be tuned arbitrarily small, the closed‐loop system has a unique solution, and all states are bounded in probability. Finally, a simulation example is given to illustrate the effectiveness of our control scheme.

Adaptive tracking control under quantized observations and observation uncertainty with unbounded variance

“…For output tracking problems of stochastic nonlinear systems, Zhu and Liu in [19] investigated a neural network adaptive finite‐time tracking control problem subject to full state constraints and presented a finite‐time control approach by using approximated‐based neural networks and adaptive back‐stepping technique. For the high‐order stochastic nonlinear systems that are perturbed by a second‐order moment process, Wang and Li in [20] considered an output tracking problem and proposed a control design method. It is worth noting that the designs of the control inputs in the literature mentioned above rely on accurate information about the system outputs.…”