Research On Fault Detection Of Nonlinear Stochastic Systems

In real systems, the controlled object or process with non-linear phenomenon existseverywhere and can not be completely eliminated. The nonlinearities not only increased thecomplexity of the system, but also made to research on the problem of analysis andsynthesis more difficulties in nature. Furthermore, the vast majority of the real system willbecome the complex stochastic system affected by the random noise. Fault detectionmethod based on the certainly system has serious limitations, it is difficult to apply tostochastic systems. Therefore, it has important theoretical significance and application valueto develop the methods for fault detection for nonlinear stochastic systems. In this paper, fornonlinear systems such as nonlinear Markovian jump systems, nonlinear stochastic systems,fuzzy systems and other complex nonlinear stochastic systems, via the probability theory,stochastic analysis, robust control and other mathematical tools, we will establish arelatively complete fault detection strategy for stochastic nonlinear systems, the mainresearch works are as follows.(1) Research on fault detection for nonlinear Markovian Jump SystemsThe fault detection for discrete-time Markovian jump systems with incompleteknowledge of transition probabilities and stochastic nonlinearities was studied in this paper.For the Markovian jumping model, the transition probability matrix is allowed to havepartially unknown entries, while with completely known or completely unknown transitionprobabilities are also studied as two special cases. For the phenomenon such as theprobability of communication failure caused by noisy environment, and the measurement offinite amplitude, the stochastic nonlinear were introduced. By constructing two energy normindicators to reflect the relationship between the disturbance and fault sensitivity, anddesigning the optimal fault detection filter, developing the new algorithm of localoptimization fault detection filter, the requirements of stochastic stability of the faultdetection dynamic system, and at the same time, the ration between the robustness indicatorof the residual signal for disturbance and the sensitivity indicators of the residual signal forthe fault signal minimize requirements were implemented.(2) Research on fault detection for stochastic time-delay nonlinear systemResearch on fault detection for stochastic time-delay nonlinear system with stochasticpacked dropouts, the considering time-delaying include multiple time-varying delaying. Themathematical model of unified characterization for stochastic packet dropouts andtime-delaying was established via the independent Bernoulli random processes. The systemwith stochastic nonlinear, stochastic occurring time-delaying and packet dropouts, via stateaugmented skills, then make the original fault detection transformed into correspondingrobust filtering, via stochastic analysis techniques, then establish the sufficient condition of the fault detection filter. In addition, by solving a convex optimization problem, gain thebest performance indicator for fault detection.(3) Research on fuzzy-model-based robust fault detection with successive packetdropoutsThe fault detection for a class of uncertain discrete fuzzy system with strongengineering background and successive packet dropouts under limited communication wasstudied. First, by building the packet dropouts model of containing the previous timemeasurement information, a unified framework was used to characterize the stochasticoccurring packet dropouts processes, by using T-S fuzzy model to approximate nonlineardiscrete-time system, then the sufficient conditions of existence of the fault detection filterwere given according to the fuzzy parameter dependent Lyapunov function approach.Auxiliary matrix introduced in the derivation processes, lifting the coupling between theLyapunov matrix and the systems matrixes, which greatly simplifies the design process offault detection filter. This part of the study provides a theoretical reference for network faultdetection of nonlinear systems.(4) Research on state observer-based fault-tolerant control of nonlinear systemsProposed a fault-tolerant control method for nonlinear stochastic systems. Forstochastic packet dropout fault from the sensor to the controller and from the controller tothe actuator in nonlinear stochastic systems, based on the estimated fault obtained fromobservations, design fault-tolerant controller, via the linear matrix inequality, make thesystem stochastic stable and ensure its H∞performance.Finally, the research work has been summarized and the further follow-up discussionand research were given.