The Study Of Estimation Problems For Stochastic Systems

This thesis aims to study the parameter estimation and state estimation prob-lems for several classes of stochastic systems. The content of this thesis is mainly divided into three parts. In the first part, we discuss the parameter estimation prob-lems for a class of linear stochastic system and a class of nonlinear nonhomogeneous stochastic system respectively, applying the filtering theory, probability theory and so on. The asymptotic properties, consistency and local asymptotic normality are studied by a set of conditions. In the second part, we consider the state estimation problem for a general class of nonlinear stochastic system with Markovian switching from the point of sample path, a series of sufficient conditions are derived which guar-antee the almost sure asymptotic stability of the dynamics of the estimation error. In the third part, we focus on the practical estimation problems in neural networks, the dynamic performance is analyzed for several class of neural networks under differ-ent engineering environment, and corresponding state estimators are designed. The compendious frame and description of the thesis are given as follows:●In Chapter1, 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 Chapter2, the parameter estimation problem is investigated for a class of linear stochastic system with noisy observations, we analyze the error covari-ance Riccati equation by Kalman-Bucy linear filtering theory and comparison theorem. Some sufficient conditions on coefficients are given to analyze the asymptotic convergence and the strong consistent property of the estimator.●In Chapter3, we study the parameter estimation problem for a class of dis-cretely observed nonlinear nonhomogeneous stochastic system, the approximate maximum likelihood estimator is given based on Euler-Maruyama numerical method, the in probability rate of convergence of the approximate log-likelihood function to the true continuous log-likelihood function is studied for the non-linear nonhomogenous stochastic system involving unknown parameter.●In Chapter4, we continue to study asymptotic property problem for a class of discretely observed nonlinear nonhomogeneous stochastic system in last chap-ter, the likelihood ratio random field is served to show the local asymptotic normality of the approximate maximum likelihood estimator. Moreover, a ver-sion of Bernstein-Von-Mises type theory is proposed through the analysis of the weak convergence of the likelihood ratio random field.●In Chapter5, a new definition, namely, almost sure state estimation is proposed and the almost sure state estimation problem is established for a class of non-linear stochastic system with Markovian switching. Then a series of sufficient condition are given which guarantee the almost sure asymptotic stability of the dynamics of the estimation error. Subsequently, some easy-to-verify procedures are put forward for the almost sure asymptotic stability in several engineering practice.●In Chapter6, the state estimation problem is investigated for a new class of discrete-time delayed neural networks with sensor saturations. An optimization method is employed to deal with the fractional uncertainties which are seldom used in neural networks, a sufficient conditions is established to guarantee the globally exponential stability for the error system based on Lyapunov stability theory and a desired state estimator is designed.●In Chapter7, we consider the robust state estimation problem for a class of discrete-time delayed neural networks with linear fractional uncertainties and successive packet dropouts. Bernoulli distribution is used to describe the phe-nomenon of successive packet dropouts, a new Lyapunov function candidate is adopted to investigate the globally asymptotically stable in mean square of the error system. Also, the robust state estimation problem is studied for the neural network.●In Chapter8, we summarize the results of the thesis and discuss some future work to be further investigated.