Filtering And Control For Nonlinear Stochastic Systems With Incomplete Measurements

In this thesis, we discuss the filtering and control problems for several classes of nonlinear stochastic systems with incomplete information. The causes of incomplete information considered here include missing measurements, sensor delays, quantiza-tion effects, sensor saturations and signal sampling. The content of this thesis is mainly divided into three parts. In the first part, we focus on the H∞, filtering and control problems for some very general classes of nonlinear stochastic discrete-time systems subject to missing measurements, quantization effects and randomly varying sensor delays. Some sufficient conditions are derived for the existence of the desired filters and controllers in terms of the Hamilton-Jacobi-Isaacs (HJI) inequalities. The robust H∞filtering problems are considered in the second part for several special classes of nonlinear stochastic systems. In this part, some novel notions, including randomly occurring nonlinearities (RONs) and randomly occurring sensor satura-tions (ROSSs), are first put forward. Then, we develop a new filtering technique for the considered nonlinear stochastic systems with RONs, ROSSs as well as packet dropouts. In the third part, the theory and technique developed in previous parts are applied to deal with some issues in both sensor networks and complex networks and some desired distributed filters and sampled-data based controllers are designed. The compendious frame and description of the thesis are given as follows:●In Chapter 1, the research background and motivation are discussed, the outline and contribution of the thesis are introduced, and the research problems to be addressed in each individual chapters are also outlined.●In Chapter 2, we investigate the quantized H∞control problem for a class of nonlinear stochastic time-delay network-based systems with probabilistic data missing, where some analysis results on the existence of the quantized H∞controller are derived in terms of HJI inequalities. Based on the analysis results, some controllers are designed for some special classes of nonlinear stochastic systems.●In Chapter 3, the H∞filtering problem is first investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements, and the existence condition of the desired H∞filter is obtained in terms of HJI inequalities. Then, the same problem is considered for the other class of non- linear stochastic systems where the phenomenon of randomly varying sensor delays is taken into account.●In Chapter 4, we study the robust H∞finite-horizon filtering problem for a special class of nonlinear discrete time-varying stochastic systems with quanti-zation effects and successive packet dropouts, where a new phenomenon, that is, RON, is proposed and a new filtering approach is developed by employing the algorithm based on the recursive linear matrix inequalities.●In Chapter 5, a new phenomenon of sensor saturation, namely, ROSS, is pro-posed and a novel sensor model is established to account for both the ROSS and missing measurement in a unified representation. Based on this sensor model, the H∞filtering problem is investigated for a class of nonlinear systems.●In Chapter 6, a new notion of H∞-consensus performance requirement is de-fined to quantify bounded consensus regarding the filtering errors (agreements) over a finite-horizon. Then, the distributed H∞-consensus filtering problem over a finite-horizon is studied for sensor networks with multiple missing mea-surements and some robust distributed H∞-consensus filters are designed by means of the solutions to a certain set of difference linear matrix inequalities.●In Chapter 7, the distributed H∞filtering problem is addressed for a class of polynomial nonlinear stochastic systems in sensor networks. The Lyapunov function candidate with form of polynomials, is first adopted to analyze the stability of the filtering error system. Then, the desired distributed H∞filters are designed by solving a set of parameter-dependent linear matrix inequalities.●In Chapter 8, the problem of distributed H∞filtering in sensor networks using a stochastic sampled-data approach is investigated. By using the method of converting the sampling periods into bounded time-delays, both of stability and H∞performance are analyzed for the filtering error system and a set of the desired distributed H∞filters is designed.●Chapter 9 is concerned with the sampled-data synchronization control problem for a class of complex dynamic networks and a set of sampled-data synchroniza-tion controllers is designed. We also consider the sampled-data H∞filtering problem for a class of stochastic genetic regulatory networks. Moreover, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon. ●In Chapter 10, we summarize the results of the thesis and discuss some future work to be further investigated.