Research On The Statistical Characterization Control For Stochastic Systems

The world is full of uncertainty.The control theory of stochastic systems has been made great theoretical achievements in the field of the low-order statistical characterization(mean and variance)over the past decades,and has been applied widely in practical engineering areas,such as aerospace,industrial production,and so on.However,the existing stochastic control method exist two problems:First,it just deals with the uncertainty such as external interference or the measurement noise which does not consider the uncertainty of system parameters.In fact,the mathematical model of the system is just an approximate model for the actual process and there is some uncertainty in parameters under some circumstances;Second,the structure of the controlled system is often considered as a linear system so the performance of the system can be realized under the control of the two low-order statistical characterization,mean and variance.However,the mean and variance are insufficient to characterize the complete features of the system for nonlinear systems.Obviously,the traditional stochastic control theory has been unable to meet the current control demands.In the dissertation,the low-order statistical characterization control for the linear systems in the presence of uncertain parameters and the complete statistical characterization control for the nonlinear systems are investigated.Some results are obtained and summarized as follows:1.For the stochastic system with multiple models,the decomposition-coordination thought of large-scale systems is introduced to the dual control of multiple models firstly.Then,use coordinational variables to integrate and normalize the control rules of multiple sub-models based on the extension of probability weighting of system parameters.Finally,utilize normalized models to control the system.The adoption of dual control method for fusion models can improve the smoothness of the process effectively.2.A suboptimal dual control method is proposed for the systems with parameters drifting.Based on the consideration of the performance index tracking and the parameter identification,the minimum variance of the system output and the estimated covariance matrix of the parameters estimation are together put into performance index to evaluate the control quality and a dual control strategy is designed which can realize the property of learning and control.3.A complete statistical characterization control problem of moments approximation is investigated for nonlinear stochastic systems.To begin with,it is assumed that the control law applied in the system is polynomial feedback of the state,and nonlinear function of dynamic equations is expanded into Taylor expansion at the same time.Then,the iterative equations of the moments for the stochastic state are derived,and the solution of the equations is the function of the control gains.At last,in order to make the shape of the PDF(Probability Density Function)track the desired form,an optimization problem is constructed and the effective complete statistical characterization control is achieved by searching for optimal control gain in gradient algorithm.4.The problem of precision PDF control for nonlinear stochastic systems is further studied.Several analyzing approaches are studied and the relationship between steady-state PDF and stochastic system is successfully deduced by the method of expanding the PDF into polynomial and exponential polynomial.Especially by the method of expanding the PDF into exponential polynomial,the precisely one-to-one correspondence relationship between Taylor expansion coefficients of exponential function and the feedback control gain to be solved is deduced.And then,the tracking control strategies of this method are respectively given according to different circumstances of target PDF.5.For a class of off-road vehicles of semi-active suspension systems,the application of multi-model dual control method which is proposed according to the thought of integration is used to conduct control research.Firstly,dynamics model of semi-active suspension system control is constructed and the corresponding continuous-time state equation is gained based on that,including the process of discretion.And then,different operating models are respectively constructed for the vehicle load condition of light load and heavy load,and the corresponding controller is designed.The effectiveness of the method is verified by simulation analysis.Finally,some concluding remarks are given,and the future research works are pointed out.