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Probabilistic Decoupling for Dynamic Multi-variable Stochastic Systems

Zhang, Qichun

[Thesis]. Manchester, UK: The University of Manchester; 2016.

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Abstract

Decoupling control is widely applied to multi-input multi-output industrial processes. The traditional decoupling control methods are based on accurate models, however it is difficult or impossible to obtain accurate models in practice. Moreover, the traditional decoupling control methods are not suitable for the analysis of the couplings among system outputs which are subjected to the random noises. To solve the problems mentioned above, we will look into the decoupling control problem in probability sense.To describe this control problem, probabilistic decoupling has been presented as a novel concept based on statistical independence. Using probability theory, a set of new control objectives has been extended by this presented concept. Conditions of probabilistic complete decoupling are given. Meanwhile, the relationship between the traditional decoupling and probabilistic decoupling has been analyzed in this thesis, theoretically.To achieve the control objectives of probabilistic decoupling, various control algorithms are developed for dynamic multi-variable stochastic systems, which are represented by linear stochastic models, bilinear stochastic models and stochastic nonlinear models, respectively. For linear stochastic models subjected to Gaussian noises, the covariance control theory has been used. The Output-feedback stabilization via block backstepping design has been considered for bilinear stochastic systems subjected to Gaussian noises. Furthermore, the minimum mutual information control has been proposed for stochastic nonlinear systems subjected to non-Gaussian noises.Some advanced topics are also considered in this thesis. The stochastic feedback linearization can be applied to a class of stochastic nonlinear systems and the reduced-order closed-form covariance control models are also presented, which can be applied in covariance control theory. Using kernel density estimation, data-based minimum mutual information control is given to extend the presented minimum mutual information control algorithm.