Research On Control Problems Of Stochastic Nonlinear Systems Based On Approximate Models

With the advancement and development of human society, the science and tech-nology improve rapidly, many advanced control theories and technologies have been applied to practical engineering and actual life, which have promoted the development of productivity and the improvement of living standards greatly. Control objects are becoming more and more complicated and intelligent, and the rapid development and popularization of information network technology, these result in that the nonlinear-ity and stochastic factors in control systems are unavoidable. The research on control problem of stochastic nonlinear systems has also drawn a lot of attention. In the real world, most of the controlled objects or plants can be modeled as continuous-time dy-namic systems, however, the system state estimation and control algorithms are usually implemented by digital electronic devices, such as computers. Thanks to the rapid de-velopment of sensor technology, computer technology and network transmission tech-nology, the computer control based on sampling control theory has been widely used in engineering practice.On the basis of the existing work and full consideration of the sampling characteris-tics existed in practical systems, this thesis mainly studies the related control problems for a class of stochastic nonlinear systems based on the discrete-time approximation model. By the discrete-time design method of sampling control theory, in this thesis,the problems of controller design and stability analysis, the discrete-time approximate observer design and convergence analysis of the observer error, the observer-based con-trol problem have been investigated based on the Euler-Maruyama approximate model of stochastic nonlinear systems. The main content can be summarized as follows:(1) The sampled-data exponential stabilization in the mean square sense for a class of stochastic nonlinear systems based on their Euler-Maruyama models is studied. For a class of continuous-time stochastic nonlinear systems that can be described by Ito stochastic differential equation, the modelling error between the exact discrete-time model of closed-loop sampled-data system and its Euler-Maruyama approximate model during one sampling period is analyzed in the mean square sense. By giving the Lya-punov theorem and Lyapunov converse theorem for the corresponding discrete-time stochastic systems, the conditions of the exponential stabilization in the mean square sense for such sampled-data stochastic nonlinear systems are established based on their Euler-Maruyama approximate model. Then, the relationship between the pth moment exponential stability of the sampled-data stochastic nonlinear system and of its exact discrete-time model is investigated. Also, the pth moment exponential stability condi-tions for a class of stochastic nonlinear systems based on their Euler-Maruyama models are obtained by extending the results derived in the mean square sense(2) The discrete-time approximate sampled-data observer design and its error con-vergence analysis for a class of stochastic nonlinear systems are discussed. For a class of continuous-time stochastic nonlinear systems which are described by Ito type stochas-tic differential equation, we assume that their output is discrete-time sampling data.Based on the Euler-Maruyama approximate model, the approximate sampled-data ob-server is designed in discrete-time framework and the convergence of observer error is also analyzed in the mean square sense. It should be noted that, the observer error of the approximate observer will be exponential convergence in practical when the system disturbance can be vanishing to zero with the system state; otherwise, the observer error of the approximate observer will converge to a bounded domain exponentially.(3) The control problem for a class of stochastic nonlinear mechanical systems based on their sampled-data observer is investigated. For a class of second-order me-chanical systems with stochastic disturbance, and the measurement output of system is discrete-time sampled-data signal. The system dynamics is modelled as a continuous-time Ito stochastic differential equation, then the approximate sampled-data observer and the observer-based controller are designed based on the discrete-time approximate model of original systems. Sufficient conditions that guarantee the exponential stabi-lization for the systems in the mean square sense are obtained, at the same time, the approximate observer error is practical exponential convergence in the mean square sense.The effectiveness of all above research results is verified by the simulation exam-ples. In the end of this thesis, we conclude our work. The keystone and difficulty of research are discussed, also, we put forward some possible research directions of future research work.