Sliding Mode Adaptive Control For Singular Stochastic Systems

Singular stochastic system(SSS)is a singular dynamical system under stochastic disturbance,which can better describe the complexity of models in practical problems.In recent years,singular stochastic systems have been widely used in circuits,electrical and power systems.As an important branch of control theory,adaptive sliding mode control is insensitive to system parameter perturbation and external disturbance,which is of great value to the study of uncertain parameters and time-delay systems.Although many scholars have studied the singular stochastic system,there are few studies on the sliding mode adaptive control of the singular stochastic system.Therefore,this paper introduces the sliding mode adaptive control of the singular stochastic system,and designs the controller to carry out the mean-square asymptotic admissibility analysis of the system.The specific work is as follows:For a singular stochastic system with actuator saturation,a sliding mode observer is designed to estimate the unknown states of the system when there are parameter uncertainties and nonlinear perturbations,so as to realize state feedback.Then,an equivalent controller is designed to stabilize the closed-loop system.By using LMI and Lyapunov function theory,it is proved that the sliding mode has finite time reachable,and sufficient conditions for the mean-square asymptotic admissibility of the closed-loop system are obtained.Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.The sliding mode adaptive control of singular stochastic systems with sensor faults is studied.Firstly,the system is augmented,and an observer is designed to estimate the system state and sensor faults,so as to realize the state feedback.Secondly,an equivalent controller is designed to enable the closed-loop system to operate stably under time delay variables and external disturbances.Finally,by using LMI and Lyapunov function theory,sufficient conditions for the asymptotic admissibility of the closed-loop system are obtained,and the performance index is satisfied.The finite time accessibility of the sliding surface is proved.