Nonlinear observation theory with applications to Markov jump systems

估计或观测一般动力系统的动力学性质（即状态）和参数的问题是系统与控制理论中的一个经典问题。从实践的角度来看，观察问题自然出现在物理系统的分析和设计中，例如生物系统和机电系统，工业过程的分析和设计，例如发酵过程和发电过程，以及网络系统，例如通信系统和电力传输系统。从理论的角度来看，观察问题出现在数学系统理论中，当人们感兴趣的是表征可以通过观察提取的信息量时，- 在自适应系统中，其中人们感兴趣的是估计要控制的系统的参数，然后利用该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操作的系统的操作模式。观察问题在以下情况下得到解决并得到很好的理解：- 基础系统是线性的或其等效于线性系统; -不考虑对状态、参数和测量的约束;- 系统不受未测量的外源信号干扰然而，如果考虑在现代工程应用中自然遇到的非线性系统和自然地对在不同状态下工作的系统建模的混合系统，可重新配置的系统或易于发生故障的系统。这些系统自然出现在生物学、电力系统和通信系统领域。该研究计划的目标是汇集两名国际公认的研究人员（PI和访问研究员），为非线性和混合系统的观测问题的解决做出贡献，特别关注所谓的马尔可夫跳跃线性系统。该计划主要是理论性的，但应用和说明性的案例研究（在故障检测和可重构系统领域）将被考虑。

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.