Estimator-Based Control for Pure-Feedback Systems With Incomplete Measurements

Abstract

This paper investigates estimator-based control problems for pure-feedback nonlinear systems with incomplete measurements due to the transmission packet losing or sensor saturation. The incomplete measurements can cause the state variables unavailable or distorted, which can degrade the performance of the system. To solve these problems, a state estimator is designed for the data-losing case, based on which two backstepping control methods are developed. The output of the system is subject to a prescribed constraint by using an obstacle Lyapunov function. By solving a linear matrix inequality, the stability conditions of the state estimator and closed-loop system are derived. It is proved that the control scheme 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 simulations. INDEX TERMS Cyber-physical system, nonlinear system, pure-feedback, controller design, incomplete measurement I. INTRODUCTION I N recent years, the control theory is making continuous progress, and the controlled system is becoming more complex. The systems integrating physical processes, computation and networking can be described as cyber-physical systems (CPSs) [1]. Many applications such as smart power grids, smart medical devices and complex physical and chemical processes can be interpreted as CPSs [2]-[6]. Because of the information exchange between subsystems, the control performance of the whole complex system has the potential to be improved. However, due to the complexity of the system, the control of the system has become a challenging problem [7]. For example, the interruption of communication between subsystems, the deterioration of communication parameters or sensor saturation will have a serious impact on the control performance and even the stability of the system [8]-[10]. Hence, many works focus on control problems of CPSs. Authors in [11]-[13] concerned about the controller design of CPSs with packet dropouts. Lu [14] proposed an input-to-state stabilizing controller for