Several results were successfully obtained regarding the estimation and control of dynamical systems under limited information. One source of limited information here considered is the case of having only infrequent and irregular data measurements available. In the context of Work Package 1, observability and detectability conditions for linear and nonlinear systems under infrequent/irregular output sampling were studied. These conditions were then exploited to propose a sample-based moving horizon estimation scheme. Moreover, event-triggered moving horizon estimation schemes were developed.
The other class of missing information considered in this project regards systems with unknown mathematical model, as proposed in Work Package 2. In this field, data-based state estimation schemes for linear systems were developed for the cases of regular and irregular output measurements. Moreover, we designed various Gaussian process-based state estimators for unknown nonlinear systems and showed how to perform inference in latent force models using optimal state estimation. Beside state estimation, we developed methods for data-based representation and control of linear systems, both in discrete-time and in continuous-time. In the discrete-time case, sample and computationally efficient data-based predictive control schemes were developed, which allow both the model of the system to be unknown and only irregular data measurements to be available. Various methods for data-based representation and control of nonlinear systems were also designed. This includes the development of a novel notion of descriptor embedding which opens new possibilities for both model-based and data-based analysis and control. Additionally, a systematic procedure to design persistently exciting inputs, allowing the collection of informative data, was obtained. Finally, computationally efficient algorithms to design data-based optimal controllers were developed.
Within Work Package 3, we extended data-driven system representation and control methods to large-scale systems by solving the multiagent synchronisation problem. Moreover, we consider optimal controllers in multiagent settings by solving nonzero sum games in a data-based fashion.
Finally, in the context of Work Package 4, predictive control schemes for the hypothalamic-pituitary-thyroid (HPT) axis were designed to determine optimal medication dosages for hypo- and hyperthyroid patients. Additionally, a mathematical model of the pituitary-thyroid feedback loop was extended, allowing an improved understanding of the origin of the Allan-Herndon-Dudley syndrome. We also investigated the preservation of detectability in approximately discretised models, which is relevant for state estimation in biomedical systems. Moreover, sample-based detectability of the HPT axis was verified, and a sample-based moving horizon estimation scheme was developed enabling the estimation of internal hormone concentrations. Finally, we studied the performance of data-based predictive control schemes for patient-specific fluid resuscitation algorithms.
All obtained results were (or are being) published in leading scientific journals and/or presented in international conferences and workshops, with the purpose of their public dissemination. So far, we obtained 34 published articles and performed 28 conference presentations and 9 workshop presentations.
