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.

Yes / This paper investigates the stabilisation problem and consider transient optimisation for a class of the multi-input-multi-output (MIMO) semi-linear stochastic systems. A control algorithm is presented via an m-block backstepping controller design where the closed-loop system has been stabilized in a probabilistic sense and the transient performance is optimisable by optimised by searching the design parameters under the given criterion. In particular, the transient randomness and the probabilistic decoupling will be investigated as case studies. Note that the presented control algorithm can be potentially extended as a framework based on the various performance criteria. To evaluate the effectiveness of this proposed control framework, a numerical example is given with simulation results. In summary, the key contributions of this paper are stated as follows: 1) one block backstepping-based output feedback control design is developed to stabilize the dynamic MIMO semi-linear stochastic systems using a linear estimator; 2) the randomness and probabilistic couplings of the system outputs have been minimized based on the optimisation of the design parameters of the controller; 3) a control framework with transient performance enhancement of multi-variable semi-linear stochastic systems has been discussed. / Higher Education Innovation Fund (No. HEIF 2018-2020), De Montfort University, Leicester, UK.