Filtering Problem For Several Classes Of Discrete Time-varying Systems In Networked Environments

This thesis discusses the filtering problem for several classes of discrete time-varying systems in the networked environment.More specifically,the networked environment under investigation not only refers to some commonly encountered network-induced phenomena(sensor saturation,signal quantization,cyber attack and event-triggering mechanism),but also covers some communication protocols,e.g.Round-Robin protocol,Maximum-Error-First Try-Once-Discard(MEF-TOD)protocol and stochastic communication protocol,which aim to prevent the occurrence of those undesired networked phenomena.The discrete time-varying systems under consideration involve parameter uncertain systems,stochastic nonlinear systems and multi-rate systems.Moreover,for the filtering problems of the addressed discrete time-varying systems,different filter design strategies are employed,which mainly include the set-membership filtering strategy,the extended Kalman filtering(EKF)scheme,the unscented Kalman filtering(UKF)approach and the H? filtering method.This thesis can be divided into three parts.The first part devotes to the investigation of the set-membership filtering problem subject to the network-induced phenomena and communication protocols in the networked environment.By virtue of the recursive linear matrix inequality(RLMI)approach,convex optimization theory,matrix decomposition method and ellipsoidal estimation theory,for the unknown but bounded noises,sufficient conditions are established to guarantee the desired filtering performance.Subsequently,by solving some convex optimization problems,the optimal filter parameters can be obtained.Then,in the second part,the Kalman filtering problem is discussed for stochastic nonlinear systems with the non-ideal network environment.First,by employing the linearization method or unscented transform(UT)approach,the nonlinear function is well handled.Then,under the standard design framework of the traditional KF,the filter parameters can be recursively solved by minimizing the filtering error covariance or its upper bound.Moreover,certain algorithms are proposed,which facilitate the online implementation.Furthermore,in the third part,the finite-horizon H? filtering issue is studied for a class of time-varying multi-rate systems with the stochastic communication protocol.By resorting to the Riccati difference equation(RDE)and stochastic analysis theories,some sufficient conditions are provided to satisfy the desired H? performance index,and the corresponding filter parameters are recursively obtained.In details,the frame of this thesis is given as follows:In Chapter 1,the research significance,research motivation and current research situation are proposed,the research problem of each chapter is introduced,and the contributions of this thesis are summarized.In Chapter 2,the probability-guaranteed set-membership filtering problem is investigated for a class of uncertain linear time-varying systems with incomplete measurements.The stochastic parameters existing in system models are assumed to obey the uniform distribution.The process noise and measurement noise are bounded but unknown.The main purpose of this chapter is to design a set of time-varying filters for all admissible bounded noises,known inputs and incomplete measurements,such that a set of optimal ellipsoidal sets is obtained by solving the optimization problem with probability constraint,which can ensure that all states are confined to the obtained ellipsoidal sets.In Chapter 3,the set-membership filtering problem is studied for a class of nonlinear time-varying systems with uniform quantization and MEF-TOD protocol.The parameter uncertainty is utilized to model the error resulted from the uniform quantization,which can be dealt by the traditional robust filtering approach.The MEF-TOD protocol with respect to the weighted measurement values is employed when the measurement output is transmitted from the sensor to the filter,which only allows one node to transmit data at each time instant,thus reducing the data conflict and increasing the reliability of data transmissions.Then,by solving the convex optimization problem with some inequality constraints,a set of ellipsoidal sets is obtained,which contains all admissible true states.In Chapter 4,the event-based distributed set-membership filtering problem is investigated for sensor networks subject to sensor saturation.Within the event-triggering mechanism,the filter is only updated when the event is satisfied,which can reduce the unnecessary data transmission between sensors and filters.The main purpose of this chapter is to design a set of distributed filters,such that for all admissible unknown but bounded noises,nonlinearities and sensor saturation,all possible true states are confined to the optimized ellipsoidal sets.By solving the recursive linear matrix inequalities,the desired filter parameters are obtained.In Chapter 5,we study the EKF problem for a class of time-varying nonlinear systems subject to the randomly occurring cyber attacks.Due to the unreliable network communication,when the data is transmitted from the sensor to the filter,it is vulnerable to cyber attacks,which can make the system performance degraded by tampering the transmission data or blocking the transmission.In this chapter,the fault data injection attack and Do S attack are simultaneously considered.Moreover,to better reflect the reality,two kinds of nonlinear functions are introduced into the system model.By solving a series of coupled Riccati-like difference equations,the desired filter parameters are obtained by minimizing certain upper bound of the filtering error.Furthermore,by utilizing the stochastic analysis theory,a sufficient condition is obtained to ensure the boundedness of the filtering error.In Chapter 6,the Round-Robin protocol-based EKF problem is discussed for a class of discrete-time stochastic nonlinear systems subject to signal quantization.Different from the method adopted in Chapter 3,the error resulted from the uniform quantization is modeled as a series of uniform distributed noises.Then,the Round-Robin protocol is introduced to schedule the network resource for the sake of reducing the data conflict and improving the reliability of data transmission.Moreover,taking the periodic property into account and by employing zero-order holders(ZOHs),the filter input is characterized by a sequence of delayed measurement outputs.Then,by means of RDE and stochastic analysis theories,the existence of the filter is obtained,and then the boundedness of the filtering error is ensured.In Chapter 7,the protocol-based UKF problem is investigated for a class of stochastic nonlinear systems subject to stochastic uncertainties.The UT is employed to deal with the nonlinear function.Moreover,during the data transmission from the sensor to the filter,the Round-Robin protocol and MEF-TOD protocol are,respectively,considered.Then,by embedding the two protocols into the UT,two protocol-based UKF algorithms are proposed.In Chapter 8,the finite-horizon H? filtering problem is investigated for a class of time-varying multi-rate systems subject to logarithmic quantization effect.The stochastic communication protocol is introduced to improve the success rate of the data transmission,which is characterized by a homogeneous Markov chain.Moreover,the sector-bounded condition is employed to model the quantization error.By using the lifting method,the multi-rate system is transformed into a single-rate one for the sake of simplifying the filter design.By solving two coupled backward RDEs,a sufficient condition is obtained to guarantee the existence of the filter parameters while satisfying the given H? performance.In Chapter 9,a conclusion is given and the future research direction is stated.