On Robust Tracking Control Of Stochastic Distribution Systems Withtime-Delays

With the development of information technology, a class of control theory, which is based on complex non-Gaussian stochastic processes, has been derived from the practical engineering. On the basis of current theories, the analysis, modeling and robust control method for the output probability density function (PDF), as the controlled object, has become one of the challenging and attractive research direction in control area. Some correlative issues in this area are studied in this thesis. The main research work and contributions of this thesis are outlined as follows:Firstly, in accordance with a class of new-type stochastic distributed continuous system with time-delay, by utilizing the approximation capability of B-spline neural networks, a simple and effective weight dynamic model is constructed, which contains both time-delay, parameter uncertainties and nonlinear terms. And then, a state feedback controller with PI structure is designed based on linear matrix inequality (LMI) theory. In addition, the stability of the proposed model is verified under the conditions of delay-dependent, at the same time, the tracking error between output PDF and designed PDF is guaranteed integral convergence under the condition of state constrained. Furthermore, combining with L1optimization measure index, the robust performance of the dynamic stochastic system is discussed. Thus, compared with the existing stochastic distributed control theory, the proposed method is an extension of the analysis of time-delay and parameter uncertainties.Secondly, for a class of discrete stochastic distributed system, evoking the approximation capability of B-spline neural networks, a novel discrete dynamic weight model is constructed, which contains state-delay. Then, a general discrete PI tracking controller is designed. Combining with linear matrix inequality theory and Lyapunov-Krasovskii stability analysis theory, a new delay-dependent stability condition is presented for the discrete stochastic distributed system. The proposed method reduces the conservativeness of the existing results of the delay-independent stability condition, at the same time, the maximum time-delay d can be obtained. Furthermore, the satisfactory state constrained tracking performance and the interference suppression performance can be guaranteed.Thirdly, the optimal tracking control problem is considered for the multi-variable coupling probability density function. Based on the definition of the conditional probability density function and the approximation capability of B-spline neural networks, the multi-objective control framework is constracted for the dynamic interconnected large-scale weight systems with time-delays. And then, a generalized PI decentralized tracking controller is designed. Combining with linear matrix inequality theory and introducing projection operator at the same time, the delay-dependent stability, tracking performance and the state constrained performance can be guaranteed. Furthermore, respectively based on L1and L2-L-infinite performance index, the problem of robust control is studied. Thus, compared with the existing stochastic distributed control theory, the proposed framework is an extension of the analysis of single probability density function.In this thesis, for the stochastic distributed system, the satisfactory tracking performance and the rubost performance can be guaranteed under the conditions of delay-dependent and parameter uncertainties. A novel tracking framework is explored for dynamic interconnected large-scale systems with multi-variable coupling probability density function. Simulation results are given to illustrate the effectiveness of the proposed control scheme.