时滞系统的可达集分析与控制

项目名称： 时滞系统的可达集分析与控制

项目编号： No.61304063

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 冯志光

作者单位： 渤海大学

项目金额： 24万元

中文摘要： 可达集分析对于系统的安全性的自动检验和系统的安全控制器的综合是十分重要的。本项目拟针对具有不同类型时滞的线性系统，包括正常状态空间系统和奇异系统，通过有效的分析与设计方法，深入研究系统的可达集分析和控制问题。首先对于正常连续线性时滞系统，通过引入新的Lyapunov函数，利用先进的不等式以及优化方法，获取保守性更小的可达集界定条件，同时给出期望控制器的设计方法，使得闭环系统的可达集界定在给定的范围内。然后通过系统变换的方法，研究连续奇异时滞系统的可达集分析和控制问题。而后通过建立离散系统Lyapunov函数界定条件，将结果推广到离散时间时滞系统。在此基础上，研究非零初始状态下时滞线性系统的可达集分析与控制问题。提供数值算例和仿真结果来检验所得结果的有效性和可行性。本项目的研究目的是，围绕时滞系统的可达集分析与控制这一主题，建立一套较为完整的理论研究成果，改进、丰富或开拓相关理论研究。

中文关键词： 可达集；时滞系统；奇异系统；马尔科夫系统；T-S 模糊系统

英文摘要： The importance of reachable set analysis lies in its utilization for the automatic verification of safety properties and for the synthesis of safe controllers for hybrid systems. This project investigates the reachable sets analysis and control problems of different kinds of time-delay linear systems including standard state space systems and singular systems by utilizing effective analysis and synthesis methods. Firstly, for standard continuous-time linear delay systems, by introducing new Lyapunov functional and utilizing the advanced inequalities and optimization approaches, less conservative conditions of reachable set estimation are proposed. The desired controller design methods are also given to guarantee the state of the closed-loop systems to be bounded in a required set. Secondly, the reachable set analysis and control problems are considered for singular time-delay systems by employing systems transformation approach. Thirdly, the results are extended to discrete-time systems with time delay by establishing the bound condition of the Lyapunov functional of discrete-time systems. Based on these results, the reachable set analysis and control problems will be studied for linear delay systems with non-zero initial conditions. Numerical examples and simulations are provided to illustrate the effectivenes

英文关键词： Reachable set；Time-delay systems；Singular systems；Markovian jump systems；T-S fuzzy systems