Backstepping control for stochastic nonlinear strict-feedback systems based on observer with incomplete measurements

Abstract

In this paper, the control problem for a class of stochastic nonlinear systems with incomplete measurements is investigated based on Luenberger-like nonlinear state observer. The systems are described as strict-feedback cyber-physical systems, in which the communication between the control centre and the physical system is subjected to disturbances. The disturbances, such as information packet losing or transmission medium saturation, cause state variables to be unavailable or distorted, which results in incomplete measurements. To solve these problems, two state estimators are designed for different transmission cases, based on which two backstepping control approaches are adopted. The stability conditions of the state estimators and closed-loop system are derived. It is proved that the control methods can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded in mean square. The effectiveness of the proposed methods is confirmed by simulation examples.

Keywords:

• Cyber-physical system
• stochastic nonlinear system
• stability analysis
• incomplete measurement

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the Scientific Research Fund of Liaoning Provincial Education Department (Grant No. 2019LNJC02), in part by Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-2017-05367), and in part by the the Funds of the National Natural Science Foundation of China (Grant Nos. 71571091 and 71771112).