面向需求差异的时滞系统稳定与控制及其应用

This project aims at developing a feature- and demand-oriented method for stability analysis and control design of time-delay systems based on the Lyapunov-Krasovskii functional method by considering the tradeoff between conservatism of the results and the rapidity of analysis. ..For the time-delay systems with low conservatism as the primary requirement, from the perspective of weakening the constraints of criteria, a systematic method of the functional construction and its derivative estimation will be investigated, and then a new delay-dependent stability analysis method with lower conservatism will be put forward to achieve the high-accuracy estimation of the time-delay margin that guarantees the stability of the systems. For the time-delay systems with low complexity as the primary requirement, from the point of the complexity of the criteria, a method for simplifying the criteria will be studied, and then a new delay-dependent stability analysis method with lower complexity will be proposed to realize the high-efficiency estimation of the time-delay margin that guarantees the stability of systems. For the control design problem of time-delay systems, a delay-dependent robust control design method will be derived by introducing the adjustable parameters to the acquisition and simplification of criteria such that the conservatism of the results and the rapidity of analysis can be adjusted as needed. The validity and superiority of the proposed theory will be verified by the applications of the power systems with communications in the loop...The project will enrich the theory of time-delay systems and also make it better to serve the practical problems. Therefore, the research of the project has significant contributions both in theoretical research and practical applications.

本项目针对时滞系统研究时结果保守性和分析快速性无法同时达到最优的问题，在分析系统特征和需求的基础上，研究基于Lyapunov-Krasovskii泛函的时滞相关稳定与控制理论方法。针对以低保守性为主需求的系统，从弱化判据条件约束的角度，建立泛函构造及其导数估计的方法，提出低保守性的稳定性分析方法，实现对保证系统稳定时滞域的高精度估算；针对以低复杂度为主需求的系统，从降低判据条件复杂度的角度，建立面向系统特征的条件简化方法，提出低复杂度的稳定性分析方法，实现对保证系统稳定时滞域的高效率估算；针对时滞系统的控制设计，在设计条件获取和简化过程引入可调参数，提出结果保守性和分析快速性按需调整的鲁棒控制设计方法。通过通讯网络在环电力系统的应用验证所提方法的有效性和优越性。本项目的研究不仅可完善时滞系统理论，而且可促使相关理论更好地解决实际问题，具有重要的科学意义和应用价值。

随着网络化控制系统的发展，大量实际系统可表示为时滞系统，时滞的存在常伴随着系统性能下降甚至不稳定。为了评估系统保持性能的允许时滞域或设计具有时滞鲁棒性的控制策略，需提出时滞相关理论方法，其保守性与复杂度分别影响准确性与高效性。.本项目提出了围绕不同需求的理论方法并将其应用于智能电网。首先，针对以低保守性为主需求的系统，提出了包括泛函构造和导数估计过程的新方法，实现了对保证系统性能时滞域的高精度估算；其次，针对以低复杂度为主需求的系统，提出了涵盖模型重构、泛函构造和相关估计等过程的新方法，实现了对保证系统性能时滞域的高效率估算；再次，针对保守性与复杂度需求变化的系统，提出了基于可调因子的模型重构、泛函构造与相关估计新思路，实现了结果准确性和分析快速性按需调整的控制设计方法；最后，将所提理论方法应用于网络在环电力系统的负荷频率控制问题。.本项目发表（含录用）高水平期刊论文26篇（包括控制领域国际顶级期刊Automatica论文1篇、IEEE汇刊论文19篇），入选ESI高被引论文3篇；项目负责人获批国家优秀青年科学基金项目、湖北省杰出青年科学基金项目，入选2022年度科睿唯安“全球高被引科学家”；培养毕业研究生5人，获中国自动化学会优秀博士学位论文奖1人次。

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