输入/输出时滞Markov跳变随机系统的最优控制与滤波

项目名称： 输入/输出时滞Markov跳变随机系统的最优控制与滤波

项目编号： No.61473134

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 韩春艳

作者单位： 济南大学

项目金额： 79万元

中文摘要： 输入/输出时滞Markov跳变系统在工程与金融领域中具有广泛的应用背景，而该类系统的最优控制与滤波是一类没有得到彻底解决的基础性问题，特别是当系统存在乘性噪声时，在当前最优控制理论中很难找到充要性研究成果。本项目将首先运用内积理论、完全配方法等技术，建立输入时滞Markov跳变线性系统的逐步优化控制方法以及输入/输出时滞Markov跳变线性系统的分离原理，给出状态反馈/输出反馈控制器的设计方法；进一步，建立一类新型随机极大值原理，研究输入时滞Markov跳变随机系统的最优控制，基于一组修正广义耦合Riccati方程，给出最优控制问题可解的充要条件和控制器的显式解析解；最后，利用Markov链重构思想、随机分析理论，建立输出时滞Markov跳变随机系统滤波问题的几何方法并给出收敛性条件。本项目的成功实施将进一步丰富时滞Markov系统的控制理论，为更广泛的工程应用提供理论依据。

中文关键词： 时滞系统；Markov跳变系统；最优控制；最优滤波；稳定性分析

英文摘要： The control and filtering for Markov jump systems with input/output delay are fundamental problems and have not been solved, especially for systems with multiple delays in single input and multiplicative noises. It have been found that such systems have more and more applications in many engineering and finance areas. This subject will devote to the control and filtering for Markov jump linear systems/stochastic systems (multiplicative noises system) with input/output delay. By employing the inner product theory and completing the square method, it will be first to establish the step-by-step optimization approach for the state-feedback controller design of Markov jump linear systems with input delays, and the separation principle for the output-feedback controller design of Markov jump linear systems with input/output delays. Furthermore, a novel stochastic maximum princeple will be established to investigate the optimal control for Markov jump systems with input delays and multiplicative noises, the existence condition for the solution and the explicit form of the Markov jump controller will given in terms of a set of modified-generalized coupled Riccati equations. Finally, the optimal filtering problem for Markov jump systems with observation delays and multiplicative noises will be solved by establishing a geometrical method based on the reorganized Markov chain and stochastic analysis theory. It will enrich the control theory for delayed Markov systems, and provide theoretical support for vast application in engineering.

英文关键词： time delay system;Markov jump system;optimal control;optimal filtering;stability analysis