Nonlinear observation theory with applications to Markov jump systems

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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.