The goal of this project is to develop estimation and control strategies for systems where only a (very) limited amount of information (measurements and models) is available. The main motivation to consider these problems are biomedical applications, where such a small amount of available information is often inherent. Examples include hormone concentration measurements when considering thyroidal diseases (which are typically only taken every few days or even weeks) or monitoring the size of a tumor. Estimating the current state of the system and devising appropriate control actions is very challenging in such applications. This is not covered by existing approaches in the literature, necessitating the development of novel methods and tools. Within this project, I will in particular focus on the following aspects. First, observability of nonlinear systems subject to few (sampled) measurements will be studied and sampling strategies together with suitable nonlinear state estimators will be derived. Second, state estimation and control strategies will be developed for situations with only partial or no model knowledge. Again, this is of intrinsic importance in biomedical applications where often the underlying physical principles are only partially understood or too complex. This necessitates the design of data- and learning-based methods, for which desired guarantees can be given, even in case of few measurements. Third, the developed tools will be extended to large-scale systems, where estimation and control has to be achieved in a distributed fashion. The successful achievement of the project goals will (i) enable estimation and control in systems with very few, sampled measurements, (ii) constitute a big step towards a holistic data-based systems and control theory, (iii) result in a new, data-driven, paradigm for the control of large-scale systems, and (iv) enable the design of systematic, personalized, and optimal control strategies in biomedical applications.
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