Interval Estimation And Fault Detection For Discrete-time Linear Parameter-varying Systems

As an important way to obtain reliable system operation data,state estimation has received extensive attention from researchers in the control field.In practice,due to un-modeled dynamics,process disturbances,and measurement noises,it is difficult to obtain accurate state estimation.Nowadays,most of the existing results on state estimation are presented based on stochastic theory.However,The methods based on stochastic theory require prior knowledge of the probability distributions of disturbances and noises,which may be deviated from real systems.In addition,it is difficult to describe some essentially nonrandom uncertainties based on the stochastic method,which limits its application.As such,a weaker assumption by modeling these uncertainties as unknown but peak-bounded perturbations may be more suitable.Such methods are called interval estimation methods.Most of the existing interval estimation methods focus on linear systems and few on nonlinear systems,which can be approximated by linear parameter-varying(LPV)systems in arbitrary precision.Thus,it is of significance to study interval estimation for LPV systems.In addition,interval estimation can estimate the feasible set of residual signals,and this set can be viewed as a dynamic threshold for fault detection.Based on the above discussion,this paper is mainly concentrated on interval estimation and related fault detection for discrete-time LPV systems.The main works and study results are as follows:The interval estimation for discrete-time LPV systems based on interval observer is studied.By incorporating a novel observer structure with more design parameters,we developed a direct design method for interval observer.To obtain a satisfactory state esti-mation performance,the effect from disturbance is suppressed via L_∞norm theory.Note that the proposed method does not require coordinate transformation,which is computa-tionally complex and may lead to overly large conservatism.The interval estimation method based on interval observer in Chapter 2 is extended to fault detection in Chapter 3.To improve the robustness to disturbance and sensitivity to fault,sufficient design conditions are derived based on L_∞norm theory and the general-ized Kalman Yakubovich-Popov(KYP)lemma.Compared to conventional fault detection observers,the proposed method can generate the envelope of output signals.Thus,faults can be detected by checking whether the real measurement is included by this envelope or not,and no external threshold generator is required.To overcome the cooperative condition required by the interval observer-based in-terval estimation method,in Chapter 4,we further develop an interval estimation method based on zonotope.First,we divide the unknown disturbance into two parts,i.e.,the part can be decoupled and that cannot be decoupled.Then,we realize the optimal inter-val estimation by decoupling the first part and propagating the rest.The proposed method combines the advantages of both conventional zonotopic interval estimation and unknown input observer and thus has better estimation performance.In Chapter 5,the method proposed in Chapter 4 is extended to fault detection.The effects caused by uncertainties and faults are respectively characterized via P-radius and finite-frequency H_-index.Suitable design parameters are obtained by solving a multi-objective problem.Compared to the method presented in Chapter 3,the proposed method does not require cooperative conditions,and thus has a wider application scope.