随机约束下非齐次Markov跳变系统控制器设计

项目名称： 随机约束下非齐次Markov跳变系统控制器设计

项目编号： No.61503155

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 刘燕卿

作者单位： 江南大学

项目金额： 20万元

中文摘要： 现代工程中大量制造系统可抽象成同时具有状态演化与事件驱动的Markov跳变系统，现有成果主要针对转移概率矩阵为常数的齐次Markov跳变系统，但工程实际中，转移概率矩阵随时间推移而变化的非齐次Markov跳变系统广泛存在，其相关理论有待进一步研究。另一方面，约束条件在实际控制器设计中不可避免，以往对约束条件的刻画，主要考虑确定性约束的描述形式，但这种形式无法刻画工程实际中广泛存在的具有随机特征的约束条件，而随机约束是以概率置信度量化的形式描述，充分体现出约束的概率信息，使得约束条件可表征的范围大大增加，具有更为广泛的工程意义。因此，研究非齐次Markov跳变系统在随机约束条件下的控制器设计具有重要意义。本项目以非齐次Markov跳变系统为切入点，基于随机规划方法，研究其在随机约束下的控制器设计方案，围绕稳定性，控制器设计，计算量与复杂度等问题展开研究，具有较为丰富的理论内涵和工程意义。

中文关键词： Markov跳变系统；随机约束；概率置信水平；非齐次转移概率

英文摘要： In modern engineering，a large number of manufacturing systems can be described as Markov jump system, which has both state-evolution and event-driven. The existing major achievements mainly focus on homogeneous Markov jump system whose transition probability matrix is constant. However, in engineering, nonhomogeneous Markov jump system, whose transition probability matrix change over the time period, is widespread. It is necessary to study its related theory. On the other hand, the actual controller design constraints are unavoidable. In the past, the constraints are described in the form of deterministic constraints, however, this form of constraints cannot describe the constraints with random characteristics, which are widespread in practice. The chance constraints are quantified by the probability given in the form of confidence, which include the information of probability . In this way, many problems in engineering can be involved in the scope of representation, and thus it is of broader engineering significance. Therefore, the study of the controller design for nonhomogeneous Markov jump system subject to chance constraints is of great significance. In this project, based on stochastic programming methods, we view nonhomogeneous Markov jump system as a starting point and study the controller design for such systems subject to chance constraints including the potential problems of stability analysis, controller design, calculation and complexity analysis. The project has abundant theoretical connotation and engineering background.

英文关键词： Markov Jump System;chance constraints;probability confidence level;nonhomogeneous transition probability