基于代数方法的切换系统状态估计算法的研究

项目名称： 基于代数方法的切换系统状态估计算法的研究

项目编号： No.61203115

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 田杨

作者单位： 南京理工大学

项目金额： 24万元

中文摘要： 切换系统作为一类重要的混合系统具有很强的理论研究意义和实用价值。目前切换系统的研究大多集中在稳定性及控制方法等方面，而切换系统的状态估计是一个亟需攻克的研究课题。本项目拟采用ALIEN代数理论，以存在外界干扰且切换时刻未知的复杂情况下的切换系统为研究对象，结合滑动视窗法，同时深入研究其他相关研究结果，旨在建立较为完整的切换系统可观性理论，最终提出有效可行的以代数逼近法为基础的切换系统状态估计方法。本项目首先将研究含有不同类型子系统 (线性定常或线性时变)的切换系统状态估计；其次根据控制输入的存在与否，分别研究自治型及受控型的切换系统；最后提供算例及仿真，检验方法的有效性。状态估计过程将以精确的数学公式表示，从而'实时'进行系统状态估算，有别于以往的为系统构造另一辅助动力系统的观测器法.该估计方法具有速度快，成本低实用性强等优点，也将为其它混合系统的状态估计提供一条新的研究方法及途径。

中文关键词： 切换系统；状态估计；切换时刻；滑动视窗；ALIEN代数逼近

英文摘要： Switched system as an important class of hybrid systems has a significant theoretical and practical value. Most current research results are focused on the stability and controllability of the switched systems, while the observability and state estimation is a key problem needed to be resolved. The project intends to apply the ALIEN algebraic theory for the switched systems subject to external unknown disturbances, under the condition of the unknown switching times. We will use the sliding window methode and study other useful existing results in order to achieve an algebraic approach for state estimation of switched systems. The state estimation of systems with different subsystems:linear time-invariant systems (LTI) or linear time-varying systems (LTV) will be firstly studied.Then secondly the controlled and autonomous switched systems will be discussed. Finally, some examples and simulations will be provided to illustrate the proposed approach. The process of estimation will be represented by an exact formula to estimate in 'real time' the state of the system, rather than by an auxiliary dynamic system.The proposed method has a fast, low-cost and practical advantage, but also provides a new way to resolve the state estimation problem for the other hybrid systems.

英文关键词： Switched systems；state estimation；switching time；sliding windows；ALIEN algebraic approach