不确定切换系统的状态和未知输入估计方法研究

The issues of state and unknown input estimation for switching system have been discussed in the existing literature, where the unknown input is not considered or considered under the assumption that unknown input matching condition is satisfied. How to break through the limit of unknown input matching condition, and put forward the unknown input observer design methods which can estimate both the states and unknown inputs for uncertain nonlinear switched systems with mismatching unknown inputs are the key issues of this project.The main contents of this project include that (1) for the switched systems without satisfying with the unknown input matching condition, some approaches which are used to break through the limit of unknown input matching condition are addressed by algebra decoupling or constructing switched auxiliary output vectors; (2) An augmented switched system is proposed where the unknown input matching condition is satisfied, and the switched unknown input observer which can estimate the states of original switched system is designed; (3)A high-gain switched sliding mode observer is given to provide the estimation of both auxiliary output and its derivative. Based on the estimation of states and auxiliary output derivative, a kind of algebra estimating method of unknown inputs is discussed; (4) The approach of unknown input observer for nonlinear switched systems is applied to fault diagnosis and chaos-based secure communication. The obtained results of this project will provide a supplement for the theory of switched system observer. Moreover, it will present new insights and methods to practical engineering problems. The study of this project is with important theoretical significance and many engineering applications.

针对切换系统的状态和未知输入估计问题，已有的研究往往是在不考虑未知输入的情形下，或考虑但未知输入匹配条件成立的假设下进行。在未知输入不匹配情况下，如何突破未知输入匹配条件的限制，提出对切换系统的状态和未知输入进行估计的未知输入观测器设计方法，是本项目要解决的关键问题。主要内容包括(1)通过代数解耦或构建切换辅助输出，研究突破未知输入匹配条件限制的方法；（2）构造未知输入匹配条件满足的增维切换系统，进而设计切换未知输入观测器，提出新的切换系统状态估计方法；(3)研究对切换辅助输出及其微分进行连续估计的高增益切换滑模观测器设计方法，在状态和输出微分估计的基础上，提出一种未知输入代数估计新方法；(4)研究切换未知输入观测器在切换系统故障诊断以及基于切换策略的混沌保密通讯中的应用。本项目有望进一步完善切换系统观测器设计理论，并为解决实际问题提供新的方法，具有重要的理论意义和工程应用价值。

控制系统状态估计和未知输入重构对状态反馈控制、故障诊断和容错控制具有重要意义。实际控制系统中，系统的状态往往不能直接测量，或由于经济的原因现有的手段难以实现，这使得设计的状态反馈控制器无法实施；此外，基于模型的故障诊断方法大多也是基于观测器设计或滤波器设计而进行的，未知信息的重构也为故障容错控制提供信息支持。本项目主要研究不确定切换系统的状态估计和未知输入重构问题，研究内容包括：（1）针对具有慢切换特性的切换信号和匹配未知输入的切换系统，提出切换信号的辨识方法，同时实现对切换系统状态的估计，研究了多切换观测器在切换信号辨识中的应用原理。（2）在系统受到扰动输出影响的情形下，基于平均驻留时间切换的概念，提出切换系统全维和降维未知输入观测器设计理论框架，实现对切换系统状态和输出扰动同时进行估计的方法。（3）研究了切换系统状态和未知输入估计方法，给出解耦未知输入的方法，以达到对系统状态估计的目的；同时，提出利用函数微分数值解估计系统输出微分，并在此基础上提出一种切换系统未知输入估计方法。（4）通过设计自适应律处理非线性项，提出非线性切换系统自适应切换观测器的设计方法，并给出切换信号应满足的条件。（5）针对遭受未知输入和执行器故障的切换系统，基于切换观测器设计理论，研究了切换系统鲁棒状态估计和执行器故障检测方法。本项目进一步完善了切换系统的观测器设计理论，为切换系统的故障诊断提供新的方法，具有重要的理论意义和工程应用价值。