Research On Control And Filtering For Non-Gaussian Systems

Control and filtering for stochastic systems have long been hot research topics in system control and signal processing. At present, control and filtering theories for linear Gaussian systems have been well developed. However, nonlinearities and non-Gaussianities exist generally in practice. The assumption that the noises are Gaussian cannot satisfy the accuracy requirements in the industrial production. For the complex stochastic dynamic systems with non-Gaussian variables, mean value and variance cannot describe the probability characteristics of the systems. In addition, with the developments of precise instrument, communication network, image processing and data processing techniques, probability distributions of system variables can be easily obtained. Actually, the probability density function contains all the information of stochastic variables. Therefore, control and filtering problems for stochastic systems have been studied by investigating the probability density function.This thesis aims to describe the probability characteristics of system parameters, initial conditions and external disturbances, and proposes new ideas and new method to solve control and filtering problems for stochastic systems. Based on the generalized minimum entropy criterion, this thesis presents the analysis results on the recursive control and filtering problems. Moreover, some of developed theories are applied successfully to the tracking problem of the networked DC motor control system and ORC based superheated vapor temperature control systems. The main research work of this thesis is listed as follows:Chapters1-3first summarize the background and existing results on the topics. Based on this, stochastic control problems are studied for nonlinear non-Gaussian systems with the constrained control input. The nonlinear ARMAX model with external disturbances are considered firstly. The probability density function of tracking error is formulated using the principle of conservation of probability without the monotonicity assumption. The quadratic Renyi's entropy is adopted to describe the probability characteristics of non-Gaussian stochastic variables and then the generalized minimum entropy principle is established. Using the penalty function method, the locally stable sub-optimal control algorithm is obtained. Moreover, a recursive probability density function evolution equation is given for nonlinear stochastic systems, where the randomness come from system parameters, initial conditions and external disturbances. The sub-optimal control law is presented by using the interior point method, and the stability condition is established in terms of linear matrix inequality. Chapter4is concerned with the controller design problem for two-input and two-output systems with external non-Gaussian disturbances. The concept of joint entropy is introduced to characterize the randomness of the non-Gaussian variables. The analytic expression of optimal control input is formulated and local stability analysis is presented.Based on the generalized density evolution equation (GDEE), Chapter5-6investigate the minimum entropy control and filtering problems for nonlinear stochastic systems with non-Gaussian noises. Since the traditional Liouville equation is difficult to solve, the GDEE theory is proposed. Firstly, the PDF evolution process of tracking error is revealed according to this equation, and the recursive control law is obtained by using the gradient descent method. The statistical linearization technique is adopted to formulate the boundedness condition of the closed-loop system. In addition, the filtering problem for nonlinear non-Gaussian stochastic systems is considered in Chapter6, and a novel filtering design approach is established in the stochastic distribution framework. By formulating the relationship between the filter error PDF and filter gain matrix, a recursive filter algorithm is designed, which can guarantee that the estimation error dynamics is exponentially bounded in the mean-square sense.In Chapter7, a new tracking control algorithm for a class of networked control systems with non-Gaussian random disturbances and delays is proposed. Since the non-Gaussian randomness involved in the systems, solely controlling the mean value of the classic linear quadratic performance index is insufficient to reflect the probability information. Therefore, higher order of the PDF of quadratic performance index should be investigated. This Chapter applies the (h,?)-entropy of the quadratic performance index to characterize the randomness of the closed-loop system. By minimizing the entropy of the performance index with Newton's method, a new control algorithm is obtained for the considered nonlinear and non-Gaussian networked control systems. In addition, the proposed control strategy is applied to a networked DC motor control system, which is subjected to non-Gaussian random disturbances and delays. The experimental results show the effectiveness of the obtained method.Considering the different demands in practical engineering, the multi-objective estimation distribution algorithm is used in Chapter8to minimize two given performance functions simultaneously. Two main purposes of the stochastic tracking control problem are presented as follows:1) minimize the magnitude of tracking error;2) minimize the randomness. Therefore, squared mean value and entropy of the tracking error are adopted as two performance indexes. Due to the nonlinearities exist in control system and performance functions, a multi-objective estimation of distribution algorithm (MOEDA) is adopted to obtain a set of Pareto optimal control inputs to satisfy the different requirements of decision makers. In this Chapter, the proposed control method is applied to an ORC based superheated vapor temperature control systems with non-Gaussian disturbances imposed on the quality of exhaust gas.