Research On Robust Control And Fault Diagnosis For Markov Jump Systems With General Transition Probabilities

With the increasement of the scale and complexity of modern control system-s,controlled objects are often subjected to abrupt changes caused by environment changes,random disturbances and the migration of working points.For this kind of system,it is difficult to get satisfactory control effects using conventional control theories based on exact quantitative mathematical model.The emergence and de-velopment of Markov jump systems(MJSs)provide an effective way to solve this problem.Markov jump systems are a class of hybrid systems which.incorporate both time-and event-driven dynamics,and the jumps among different modes are described by a Markov process.Transition probability,as a critical factor,affects the stabilization of Markov jump systems.However,the exact information about the transition probabilities is often insufficient or even lacking in practice due to the existence of various uncertainties and the limitation of measurement-techniques.Specially,general transition probabilities allowed to be unknown and uncertain is more general than completely known or completely uncertain transition probabil-ities,which attract peoples' attention.Up to date,the research on Markov jump systems with general transition probabilities is also not deep and thorough,pending further study.This dissertation further studies the problems of controller design and fault diagnosis for Markov jump systems with general transition probabilities.The quan-tized state feedback control problem as well as the quantized dynamic output feed-back control problem for Markov jump systems with general transition probabilities is studied,and controller design conditions of less conservativeness are given.For large-scale Markov jump systems with general transition probabilities and unknown interconnections,a method for designing decentralized dynamic output feedback controllers is proposed by introducing a cycle-small-gain condition.For large-scale Markov jump systems with measurement errors,a new approach for designing neigh-boring mode dependent decentralized dynamic output feedback controllers is pro-posed.Further,the decentralized fault detection and isolation problem for large-scale Markov jump systems with unknown interconnections is investigated based on neighboring mode dependent decentralized fault detection filters.In addition,for a class of nonlinear Markov jump systems with general transition probabilities,a fault estimation method based on intermediate observer is developed.Some theoretical results are applied to the F-404 engine model,the 3-machine-9-bus power system model and the VTOL aircraft model.Simulation results show the effectiveness of the proposed methods.The main contents of this paper are as follows:In Chapter 1-2,the development and main research methods of Markov jump system theory are analyzed and summarized,and some preliminaries about the considered problems are given.In Chapter 3,the problem of quantized feedback control for Markov jump sys-tems with general transition probabilities is investigated.It is the first time to present H? state feedback controller design method for Markov jump systems with general transition probabilities and mismatched quantization parameters.By ex-ploiting a vertex separator,sufficient controller design conditions are developed in the formulation of linear matrix inequalities.Then by introducing slack variables,a new method for designing H? dynamic output feedback controller is presented considering the matched quantization parameters.The proposed method is less conservative than the existing methods.Simulation results show the effectiveness and merits of the proposed methods.In Chapter 4,the problem of decentralized dynamic output feedback control for Markov jump large-scale systems with general transition probabilities and unknown interconnections is studied.Based on local measurements,a decentralized dynamic output feedback controller is constructed for each subsystem,and a cycle-small-gain condition is introduced to deal with unknown interconnections such that the resultant closed-loop system is stochastically stable with an H? performance.Then,the controller design conditions with less conservativeness are presented in the form of linear matrix inequalities.Simulation results show the effectiveness and merits of the proposed method.In Chapter 5,the problem of decentralized dynamic output feedback control for Markov jump systems with measurement errors is addressed.By utilizing local measurements and neighboring mode information,a decentralized dynamic output feedback controller is constructed for each subsystem.Then,a new design method is proposed such that the resultant closed-loop system is stochastically stable and satisfying an L? condition.By introducing a cycle-small-gain condition and slack variables,the controller design conditions are presented in the formulation of linear matrix inequalities.The benefit of the proposed approach is in the fact that,for each local controller,the requirement for access to operation modes of all subsystems is removed.Simulation results show the effectiveness and merits of the proposed method.In Chapter 6,the problem of decentralized fault diagnosis for Markov jump large-scale systems with unknown interconnections is investigated.Firstly,a decen-tralized fault detection filter is constructed to generate a residual for each subsystem by utilizing local measurements and neighboring mode information.And then a nov-el design method is developed such that the generated residual is sensitive to local fault and robustness to disturbance.Further,an effective fault detection scheme is proposed.In contrast to the existing methods,the proposed method can avoid the requirement for access to operation modes of all subsystems,and can achieve fault detection and fault isolation simultaneously.Simulation results show the effective-ness and merits of the proposed method.In Chapter 7,the problem of fault estimation for a class of nonlinear Markov jump systems with general transition probabilities is studied.Based on interme-diate variables,mode-dependent intermediate estimators are presented.Then,a new design method which is less conservative is proposed based on linear matrix in-equality technique.The design guarantees the stochastic stability of the estimation errors when there is no fault and the boundeness in probability if the derivations of the faults are bounded.Simulation results show the effectiveness and merits of the proposed method.Finally,the results of the dissertation are summarized and further research topics are pointed out.