Research On Identification And Stabilization Of Nonlinear Continuous-time System And Stochastic System

The stabilization problem and the identification problem of both nonlinear continuous-time systems and stochastic systems are studied in this dissertation. The following are the main results:First the output-feedback stabilization problem of both nonlinear continuous-time systems and stochastic systems are studied, the robust output-feedback stabilization of a class of nonlinear systems with the nonlinearities of varied form, confined by a smooth function, is realized by backstepping designs; The high-gain observer stabilization of a class of nonlinear systems without the rigid feedback condition is discussed and the regulation domain of the controller parameter is extended; The robust output-feedback stabilization (in probability) of a class of stochastic systems is realized by using the high-gain observers, not limited on rigid feedback systems, the more general stochastic systems can be stabilized in this way.Secondly, the stabilization in distribution of stochastic systems is studied, a sufficient condition of the existence of probability density function of diffusion processes is obtained,the stabilization in distribution of a stochastic system is defined; The stabilizer in distribution of one-dimensional stochastic system is obtained by using canonical probability theory method for both the additive gauss noise system and the multiplicative gauss noise system, the controlled state has the designed asymptotic probability density function.Thirdly, the identification problems of both the stochastic nonlinear processes and the MIMO nonlinear continuous-time systems are studied, an approach of model identification is suggested for a class of stochastic nonlinear processes, the maximum likelihood estimates of the model parameters are derived based on continuous sampling, the convergence analysis and the evaluation method of the estimates are given, the decentralization of the estimates deduces the desired identification algorithms; As a control-oriented identification, an identification approach for a type of two-input two-output nonlinear continuous-time system with observable states using driving sign is suggested, the driving sign is Gauss white noise, the output are sampled evenly, the maximum likelihood estimates of the model parameters are derived by using the Girsanov theorem, the convergence of the estimates are proved, and the NNR (noise ratio of one state to another) phenomenon of coupling multi-variable system identification appears in the numerical simulations.Finally, Applications of stable probability density function to image processing and biology modeling are given, a threshold segmentation algorithm based on the normal distribution forecast is proposed, which improved Ostu algorithm without increase the computation quantity; A criterion of stability in distribution of stochastic logistic multiplicative noise model is obtained with the formula of the asymptotic probability density function, thus dynamics simulations of the state probability density function is realized.