Estimation and control under limited information with application to biomedical systems

Project Information

Cont4Med

Grant agreement ID: 948679

DOI

10.3030/948679

Project closed

EC signature date 12 October 2020

Start date 1 January 2021

End date 31 December 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 497 965,00

EU contribution

€ 1 497 965,00

Coordinated by

GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER
Germany

Periodic Reporting for period 4 - Cont4Med (Estimation and control under limited information with application to biomedical systems)

Reporting period: 2025-07-01 to 2025-12-31

Summary of the context and overall objectives of the project

The goal of this project is to develop estimation and control strategies for dynamical systems where only a very limited amount of information is available. This information includes current measurements of the system as well as a mathematical model. The main motivation for considering 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 several days/weeks) or monitoring the size of a tumour. Estimating the current state of the system and devising appropriate control actions (e.g. therapy or medication in the biomedical examples) is very challenging in such applications.

Achieving these objectives requires the development of novel methods and tools. Within this project, particular focus lies on the following aspects.

First, we study under which conditions is it possible to reconstruct the full internal system information using only few output measurements. Sampling strategies and suitable nonlinear state estimators are derived.

Second, state estimation and control strategies are developed for situations with only partial or no knowledge of a mathematical model of the system in question. This necessitates the design of so called data- and learning-based methods, for which desired guarantees can be given, even in case of few measurements.

Third, the developed tools are extended to large-scale systems, where estimation and control has to be achieved in a distributed fashion.

The results that have been obtained within this project
(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 optimal control strategies in biomedical applications.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

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.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The results described above have advanced the state of the art in the areas of data- and learning-based control and estimation, estimation with irregular and infrequent measurements, and modeling and control of biomedical systems (mainly the HPT axis).

In particular, a theoretical result known as Willems' fundamental lemma was exploited to design robust state estimators that do not require model knowledge and allow to consider state constraints (like, e.g. nonnegativity constraints of hormone concentrations). We also exploited learning techniques (in particular, Gaussian processes) to design novel state estimators for unknown, noisy nonlinear systems. In this case, we also contributed to the learning literature by analysing GP training with noisy regression inputs. Similarly, extensions of the fundamental lemma were developed and used to design novel control methods for some classes of nonlinear systems with provable stability guarantees. To this end, systematic methods to design input signals that persistently excite certain classes of nonlinear systems were proposed for the first time. Furthermore, a novel extension of Willems' lemma allowing the data-based representation of continuous-time systems was developed and used for data-driven control. This result was extended for the data-based representation and control of multiagent systems.

Moreover, our contributions allow to estimate the internal system state from only few and irregular output measurements. These results are of intrinsic importance for the biomedical applications that motivate the developments of this project.

Finally, in the context of the HPT axis, optimal medication strategies have been developed for different thyroidal diseases and the impact of different medication strategies were analysed using modern control-theoretic tools.

The results obtained in this project open up many interesting topics of future research, ranging from the advancement of data- and learning-based control and estimation, to the design of personalised treatment schemes in biomedical applications.

Overview of the Project Cont4Med