Recursive Filtering And Controller Design For Nonlinear Stochastic Systems In Networked Environments

Stochastic control and filtering have been one of the main stream of research topicsin control field. Up to know, the control and filtering theories for linear systems havebeen well developed. However, the study on the control and filtering for the nonlinearstochastic systems needs to be further investigated, and there still exists many importantyet difficult problems which needs to be solved. On the other hand, with the extensiveapplications of the networked control systems (NCSs), the existence of network-inducedphenomena brings many new challenges to the study of control theory research. There-fore, it has wide applications and more challenge to develop some novel control andfiltering methods for the nonlinear stochastic systems over network.The content of this thesis is mainly divided into four parts. In the first part, we dealwith the recursive filtering problems for several classes of nonlinear time-varying stochas-tic systems with missing measurements, random sensor delays, quantization effects andcorrelated noises. The optimal recursive filter gains are obtained in terms of the solutionsto the Riccati-like difference equations. Some proposed results have been applied to thestate estimation of the target tracking systems. The problem of finite-horizon probability-guaranteed H_∞filter design is considered in the second part for a class of nonlinear time-varying stochastic systems with sensor saturation. Based on the difference linear matrixinequality (DLMI) technique, the sufficient condition is presented to guarantee the ex-istence the recursive filter with the desired probability performance. In the third part,the phenomena of randomly occurring actuator failures (ROAFs) and fading performanceoutput (FPO) are first put forward and the mathematical models are introduced. Then, theguaranteed-cost reliable control problem is studied for a class of nonlinear time-varyingstochastic systems with ROAFs and FPO. Finally, the definition of randomly occurringuncertainties (ROUs) is put forward and the mathematical model is introduced. The robustsliding mode control problems are investigated for several classes of uncertain nonlinearstochastic systems with time-varying delays. The main contents are given as follows:The research background and significance are reviewed about the recursive filteringand control for nonlinear stochastic systems over network. Subsequently, the existingdescriptions of the network induced phenomena and the recent advances on the filtering and control of the nonlinear stochastic systems are summarized. Moreover, the significantproblems to be further studied in the filtering and control with network induced phenom-ena are pointed out. Finally, the main contents of this thesis are discussed.The uncorrelated noises with known statistical properties is considered and the re-cursive filters are designed for nonlinear time-varying stochastic systems. The missingmeasurements are modeled by a series of mutually independent random variables obey-ing Bernoulli distributions with individual conditional probabilities. The recursive filter-ing problem is studied for a class of nonlinear time-varying stochastic systems subject tomultiplicative noises, missing measurements and quantization effects. An upper boundfor the filtering error covariance is guaranteed and such an upper bound is subsequentlyminimized by properly designing the filter gains at each sampling instant. The developedalgorithm is used to the state estimation of the ballistic object tracking system. More-over, the phenomena of multiple missing measurements are characterized by employingan a series of random variables with any discrete probability distribution over the interval[0,1] and known conditional probabilities. Then, the extended Kalman filtering problemis investigated for a class of nonlinear time-varying systems with stochastic nonlinearitiesand multiple missing measurements. The desired filter gains with the recursive form areobtained in terms of the solutions to two Riccati-like difference equations.The correlated noises with known statistical properties is considered and the recur-sive filters are designed for nonlinear time-varying stochastic systems. The phenomenaof multiple fading measurements are characterized by introducing a series of mutuallyindependent random variables obeying any discrete probability distribution over the cer-tain interval with individual conditional probabilities. By constructing a new Kalman-like filter, the recursive filtering problem is solved for a class of nonlinear time-varyingstochastic systems with correlated noises and random parameter matrices. By employingthe Riccati-like difference equation approach, the filter gains are given in the minimumvariance sense. Moreover, the random sensor delays are modeled by a series of mutu-ally independent random variables obeying Bernoulli distributions with individual condi-tional probabilities. The gain-constrained recursive filtering problem is studied for a classof nonlinear time-varying stochastic systems with random sensor delays and correlatednoises. The developed algorithms are employed to deal with the problems of the stateestimation for target tracking systems. An algorithm of filter design is developed such that the H_∞performance require-ment is satisfied under certain desired probability. The uncertainties of the system pa-rameters are characterized by a series of mutually independent random variables obeyingthe uniform distributions over known finite ranges. The sensor saturation is transformedto an easy-to-implement form by employing the sector-bounded approach. By means ofstochastic analysis, the probability-guaranteed finite-horizon H_∞filtering problem is dis-cussed for a class of nonlinear time-varying stochastic systems with uncertain parametersand sensor saturations. Sufficient conditions are established to ensure that the H_∞perfor-mance is satisfied under desired probability, and the recursive algorithm is developed toobtain the time-varying filter gains.The guaranteed-cost reliable control problem is studied for a class of nonlinear time-varying stochastic systems ROAFs and FPO. The phenomena of ROAFs are modeled byintroducing a random variable obeying the Bernoulli distribution with known conditionalprobability. Moreover, the phenomenon of fading performance output is characterized bya random variable satisfying any discrete probability distribution with known conditionalprobability. For the pre-defined cost function, the recursive form of the controller gainsare given in terms of the solution to a Riccati-like difference equation. Also, an optimizedupper bound of the pre-defined cost function is guaranteed by employing the developedcontrol scheme.The robust sliding mode control problems are investigated for two classes of uncer-tain nonlinear systems with time-varying delays. The phenomenon of randomly occurringnonlinearity (RON) is modeled by introducing a random variable obeying Bernoulli dis-tribution with known conditional probability. The sliding mode control problem withtime-varying delays and RON is studied. For the specified sliding surface, the slidingmode control law is designed to ensure the discrete sliding mode reaching condition. Byemploying the delay-fractioning approach, sufficient conditions are given such that thesliding mode dynamics is exponentially mean-square stable. Moreover, according to theLyapunov method and linear matrix inequality technique, the robust H_∞sliding modecontrol problem is investigated for a class of uncertain systems with time-varying delaysand stochastic nonlinearity.The robust sliding mode control problems are studied for two classes of uncertainnonlinear stochastic systems with mixed time-delays. By introducing two series of mutu- ally independent random variables, the phenomena of ROUs and randomly occurring non-linearities (RONs) are modeled respectively. The design of robust sliding mode controlleris investigated for nonlinear stochastic systems with ROUs, RONs and mixed time-delays.For the specified sliding surface, by constructing a novel Lyapunov-Krasovskii functionalbased on the delay-fractioning idea, sufficient conditions are presented such that the slid-ing mode dynamics is asymptotically mean-square stable. Then, the sliding mode controllaw is synthesized to guarantee the discrete sliding mode reaching condition. Moreover,by employing the delay-fractioning approach, the robust sliding mode control problem isstudied for a class of uncertain nonlinear systems with Markovian jumping parametersand mixed time-delays.