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Nonlinear observation theory with applications to Markov jump systems

非线性观测理论及其在马尔可夫跳跃系统中的应用

基本信息

批准号：
EP/E057438/1
负责人：
Alessandro Astolfi
金额：
$ 10.09万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FE057438%2F1
关键词：
Nonlinear observation theory applications Markov

项目摘要

The problem of estimating or observing the dynamical properties (i.e. the state) and the parameters of a general dynamical system is a classical problem in systems and control theory. From a practical point of view the observation problem naturally arises in the analysis and design of physical systems, such as biological systems and electromechanical systems, of industrial processes, such as fermentation processes and power generation processes, and in networked systems, such as communication systems and power transmission systems.From a theoretical point of view the observation problem arises in- mathematical systems theory, where one is interested in characterising the amount of information that can be extracted by means of observation (over a time interval or at sampled instants);- in adaptive systems, where one is interested in estimating the parameters of a system to be controlled and then in exploiting this information to achieve some control objective;- in the theory of hybrid systems, where the problem is to single out the mode of operation of a system that can operate in several different modes.The observation problem is solved and very well understood under the following circumstances: - the underlying system is linear or it is equivalent to a linear system; - constraints on the state, parameters and measurements are not taken into considerations;- the system is not perturbed by unmeasured exogenous signals (disturbances).However, the problem is much more involved if one considers nonlinear systems, which are naturally encountered in modern engineering applications, and hybrid systems, which naturally model systems working in different regimes, reconfigurable systems or systems prone to failures. These systems naturally arise in the areas of biology, power systems, and communication systems.Goal of this research programme is to bring together two internationally recognized researchers (the PI and the visiting fellow) to contribute to the solution of the observation problem for nonlinear and hybrid systems, with special attention to the class of so-called Markov-jump linear systems. The programme is mainly of a theoretical nature, but applications and illustrative case studies (in the areas of fault detection, and reconfigurable systems) will be considered.

估计或观察一般动力系统的动态特性（即状态）和参数的问题是系统和控制理论中的经典问题。从实际的角度来看，观察问题自然出现在物理系统的分析和设计中，如生物系统和机电系统，工业过程，如发酵过程和发电过程，以及网络系统，如通信系统和电力传输系统。从理论的角度来看，观测问题出现在数学系统理论中，人们对通过观测（在一段时间间隔内或在采样时刻）可以提取的信息量的特征感兴趣；-在自适应系统中，人们感兴趣的是估计被控制系统的参数，然后利用这些信息来实现某些控制目标；-在混合系统理论中，问题是挑选出可以在几种不同模式下运行的系统的运行模式。在以下情况下，观测问题得到了解决并得到了很好的理解：-底层系统是线性的或相当于线性系统；-未考虑状态、参数和测量的约束；-系统不受未测量的外源信号（干扰）的干扰。然而，如果考虑现代工程应用中自然会遇到的非线性系统和混合系统，那么问题就更加复杂了，混合系统自然会对在不同制度下工作的系统、可重构系统或容易发生故障的系统进行建模。这些系统自然出现在生物、电力系统和通信系统等领域。本研究计划的目标是将两位国际公认的研究人员（PI和访问研究员）聚集在一起，为非线性和混合系统的观测问题的解决做出贡献，特别关注一类所谓的马尔可夫跳变线性系统。该方案主要是一个理论性质，但应用和说明性的案例研究（在故障检测和可重构系统的领域）将被考虑。