Fault Detection For Several Classes Of Markovian Jump Systems Via The Incomplete Observations

The fault detection problem of Markovian jump system is one of the hot issues in current research,and it has important applications in the fields of aerospace,shipbuilding,and small control machines.Related research methods can enable the system to alarm when the potential failures occur caused by complex situations,and to analyze the impact onto the system performance due to the environment and human factors.Therefore,it is very important to design an effective fault detection filter algorithm to ensure the normal operation of the system.In fact,due to sudden changes caused by external disturbances or some unpredictable causes in the actual environment,the structure of the system will change,and it is necessary to introduce a suitable mode-dependent Markovian jump system.On the other hand,considering the influence of the network induced phenomena(e.g.,the event-triggered protocol,measurement missing,signal quantization),the fault detection filter can't receive all transmission information.Therefore,the study of fault detection based on the available effective observation information for the system has important theoretical research significance and value.The aim of this thesis is to design the fault detection filtering algorithms for some classes of uncertain Markovian jump systems with network-induced phenomena.The detailed contents are summarized as follows.Firstly,the fault detection problem is studied for a class of discrete time-varying Markovian jump systems with quantization and missing measurement.The phenomenon of missing measurement is described and the measurement output is quantized by a logarithmic quantizer.Based on the available information,a fault detection filter is designed and the residual signal is obtained via the filter.Next,by using the stability theory and stochastic analysis method,the sufficient conditions are given to ensure the stochastic stability of the augmented system.In addition,the expression form of filter gain matrix is obtained.Finally,the simulation results are given to verify the effectiveness of the proposed fault detection strategy by using the Matlab Software.Secondly,the fault detection problem is discussed for the nonlinear uncertain Markovian jump system under event-triggered scheme.In order to reduce the network transmission burden and save network resources,an event-triggered mechanism is introduced.During the modeling process of system,assume that the nonlinear function satisfies the Lipschitz condition and the modeling error is characterized by the norm-bounded uncertainty.Based on the output information of the system,an effective fault detection filter is constructed.Then,by using the linear matrix inequality technique,sufficient conditions are given to guarantee the stochastic stability of the system and the existence of the desired filter gain matrix.Besides,the forms of filter gains are obtained.Finally,the effectiveness and feasibility of the proposed algorithm are verified by employing the numerical simulation.Thirdly,the non-fragile fault detection problem is investigated for a class of nonlinear discrete time-varying Markovian jump system under a dynamic event-triggered mechanism.The known and partially unknown situations of the Markovian state transition probability matrix are considered.In addition,the dynamic event-triggered communication mechanism is introduced.Compared with the static event-triggered mechanism,the dynamic event-triggered mechanism can reduce the possibility of data transmission congestion.Based on the measurable information of the system,a new fault detection filter is constructed.Then,sufficient conditions are given to ensure the stochastic stability of the system and the existence of the filter gain matrix.Subsequently,the desirable filter gain matrices are designed to realize the fault detection scheme.Finally,numerical examples are provided to verify the effectiveness of the proposed fault detection algorithm.Fourthly,the finite-time fault detection problem is investigated for Markovian jump system with incomplete measurement information under a dynamic event-triggered mechanism.In particular,the incomplete measurement information is characterized by introducing an interval matrix representation method with uncertainty.Based on the measurable output information,a fault detection filter is constructed and the occurrence of a fault can be detected by the obtained residual signal.Then,the sufficient conditions are given to guarantee the system to be stochastically finite-time stable and satisfy the finite-time performance index,where both the cases of the state transition probability matrix with known and partially unknown probability are considered.Subsequently,the filter gain matrices are obtained by using the inequality analysis technique.Finally,the numerical simulation is presented to verify the effectiveness of the proposed finite-time fault detection algorithm.