Further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems

Abstract

This paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems. Comparing with the existing relevant literature, the systems under investigation allow more serious unknowns/uncertainties. More importantly, by remarkably reducing the dimension of dynamic compensator for system unknowns (from n to 2) and considerably diminishing the overparametrisation in the existing literature, this paper proposes an improved design scheme for adaptive state-feedback controllers. It is turned out that, with the designed controller in loop, all the closed-loop system states are globally bounded and the original system states converge to the origin, both in the sense of probability one. A simulation example is also given to demonstrate the effectiveness of the theoretical results.

Keywords:

• high-order stochastic nonlinear systems
• stochastic integral input-to-state stable
• adding a power integrator
• global adaptive stabilisation

Additional information

Funding

This work was supported by the National Natural Science Foundations of China [grant number 61403348], [grant number 61325016], [grant number 61273084], [grant number 61233014]; the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China [grant number JQ200919]; and the Independent Innovation Foundation of Shandong University [grant number 2012JC014].