Modeling And Predictive Control Of Non-Guassian, Non-stationary System

This paper focus on modeling and predictive control of non-Gaussian and non-stationary stochastic system.(1) Non-Gaussian:The distribution of the parameters in the system isn't Gaussian distri-bution.f(·) dose not follow Gaussian distribution;(2) Non-stationary:The probability characters of the random variables are time variance. ?k is time variance, which can influence the shape of the probability density functionsThis kind of stochastic system can be found in zoology, medicine, industry, finance and so on. So it is meaningful to study the problems of modeling and predictive control of non-Gaussian and non-stationary stochastic system.Classical input and output models (such as autoregression model) and state-space model are often used to model stochastic systems. But in non-Gaussian, non-stationary stochastic sys-tem, the methods to estimate the parameters and the structure of these models are too complex. And it is hard to apply in predictive control of non-Gaussian, non-stationary stochastic system. So these two models are difficult to directly apply to model non-Gaussian and non-stabilization stochastic system. To solve this problem, the researchers study and apply GLM (Generalized lin-ear model) in time series modeling. However, GLM is only applicable to the exponential family which includes the Gaussian distribution and Poisson distribution, etc., and only can model the mathematical expectation and variance of parametric. To overcome this problem, we propose generalized time series model (GTS). This model is not subjected to the constraints of the dis-tribution of species hypothesis. In addition, we can model the parameters which influenced the probability density characteristics, like mathematical expectation, variance and so on. So, this model can well reflect the non-stationary characteristics of random variables.Because of non-Gaussian distribution, we use the maximum likelihood to estimate the pa-rameters of the models. On the basis of determining the model structure and estimation methods, model evaluation and selection is an important task. We use a new coefficient of determination to evaluate model fitness to the data. Furthermore, we propose a BIC-based hierarchical selection algorithm to investigate the optimal structures for GTS.In the process industry, simply controlling the expectation and variance of the output has been unable to meet the needs of industrial anymore. Researchers don't research the output directly anymore, they focus on shape of probability density function (PDF) of the output, which is called PDF control. In this paper, we proposed a new predictive control method by combing GPC with GTS.In this paper, we describe the non-stationary stochastic system with time invariant param-eters. The GTS model we proposed in this paper is not subjected to the constraints of the distri-bution of species hypothesis. We can use it to describe any PDF. In this paper, we research the predictive control of non-stationary stochastic system.