Reachable Set Estimation Methods For Discrete-time Systems And Their Applications In Fault Detection

As informatization and networking progresses in society,The modern control systems are developing in the trend of scale,complexity and refinement.In order to ensure the stability and proper functioning of the control systems,the estimation methods for unmeasurable signal have been widely concerned in recent years.Different from the interval estimation methods,the reachable set estimation obtains the bounded region of all reachable states of the signal,which usually has higher accuracy.Based on the Lyapunov stability principle,the existing methods estimate the reachable set by solving the linear matrix inequalities,which have advantages ocalculation and optimization design.However,most of the proposed methods have limitations and can be improved in real-time and applicability.In recent years,more attention has been paid to the reachable set estimation based on zonotopic technique,which applies linear mapping iteration to obtain more accurate results.However,the methods based on zonotopic technique usually have the disadvantage of intensive computation.In this paper,these two kinds of reachable set estimation methods are studied and applied to fault detection.The main work and research results are as follows:The reachable set estimation method based on system stability is studied.By applying Lyapunov stability principle,the proposed method can estimate the reachable set in real time,and is applicable for systems under non-zero initial conditions and parameter uncertainties.The multi-objective optimization conditions are designed to make the estimated reachable set satisfy the initial value optimal and steady-state optimal conditions.In addition,a system separation method is proposed to separate the system into the known terms and unknown terms,which can reduce the conservatism caused by the known terms.A real-time reachable set estimation method for time-delay systems with parameter uncertainties is proposed,and is extended to uncertain nonlinear systems with time-delay to make it more general.In addition,a Lyapunov-Krasovskii functional is derived for obtaining a real-time reachable set estimation method for uncertain nonlinear systems with time-varying delay.A method to estimate the reachable set for discrete-time delay systems is proposed by using zonotopic technique.Based on the basic properties of zonotopes,an order reduction algorithm is proposed to reduce the iterative computation.At the same time,an approach to estimate the reachable set for time-varying delay systems based on zonotope interval box is proposed.In addition,the proposed method is extended to bilinear time-delay systems.The proposed reachable set estimation method is applied to actuator fault detection.Based on Lyapunov stability principal and zonotopic technique,respectively,two fault residual evaluation methods are proposed.The proposed fault detection methods are extended to time-delay systems and nonlinear systems for expanding the application scope.