PhD student (M/F) – Thesis topic: Stabilisation and control under resource constraints

Job Description

Thesis Subject

Abstract: Future generations of safety-critical control systems will have to operate under multiple constraints. These constraints relate both to internal states, which must remain within permissible ranges (for example, biological concentration, fuel level or battery charge must remain positive), and to actuators, which are always subject to saturation limits. Overall control resources (energy reserves, fluids or any other consumable resources) are also necessarily limited. Numerous applications illustrate these challenges, whether it be closed-loop insulin delivery ('artificial pancreas'), the control of autonomous drones, or various biological, ecological or technical systems. Taking such constraints into account in the design of control laws is, to a certain extent, well established.
However, in many cases, available resources are only available for a limited period, or safety considerations require that their use be restricted to a fixed time horizon. This is precisely the case for any control problem involving limited resources during a mission (insulin or fuel reserves, battery power, etc.). These constraints could be referred to as 'memory constraints', as they govern the evolution and availability of resources over time. Such constraints raise challenges that remain unexplored in the literature. The aim of this thesis is to analyse their impact and to develop a methodological framework enabling them to be rigorously integrated into the design of critical control systems. ** Research question and general context: The study of control problems with strict integral constraints is crucial, as it reflects the limitations of the real world. In many situations, such as drug administration, energy management or engineering systems with limited resources, there are strict limits on the amount of resources that can be consumed over a given period of time. Conventional control designs generally ignore these limitations, which can lead to solutions that are mathematically optimal but unfeasible in practice. In this work, the limited nature of resources is expressed as a constraint on the time integral of the control. More specifically, over a fixed time horizon, the integral of the control must remain below a given constant. The objective is to design control laws that guarantee stabilisation in the presence of such constraints. However, it is not known how to systematically construct a stabilising feedback with an integral limit, whether feedback solutions always exist, and under what conditions 'bang-bang' or saturating behaviour occurs. The problem of designing control laws under integral constraints has been addressed mainly in the context of optimal control. For example, in his work on pharmacokinetics [2], Bellman formulated constrained dosing problems and demonstrated how dynamic programming could be used to guarantee integral bounds. Motivated by the need to plan flights with a limited fuel supply, the problem of 'minimal fuel control' has been studied; see [1, Chapters 6 and 8]. These problems are similar to integral constraints, with an emphasis on efficiency and resource management. These studies have utilised tools based on linear programming [5] and approaches based on PDEs [3,4]. However, these approaches do not directly address a more practical question: how can a target trajectory be tracked or stabilised whilst ensuring that the total available control effort is not exceeded? This shortcoming warrants a more in-depth examination of control law structures and synthesis methods within the framework of integral constraints.
Here are some open questions being considered for the thesis: -- Under what conditions is the system controllable? If it is not controllable, can the reachable states be characterised; in particular, are steady-state states controllable? -- To achieve control, it is natural to seek a control that minimises a cost function. What are the conditions for optimality? Can Pontryagin's maximum principle be applied in this case? -- Can we construct a feedback law that stabilises the system whilst satisfying the constraint? Can it also minimise a cost? Can Lyapunov theory be used to find a feedback law?
Quote : [1] M. Athans et P. L. Falb. Contrôle optimal. Série McGraw-Hill d'ingénierie électrique et électronique. McGraw-Hill Book Company, New York, NY, 1966. [2] R. Bellman. Thèmes de pharmacocinétique, III : Dosage répété et contrôle impulsionnel. Math. Biosci., 12(1):15, 1971. [3] A. Kumar et A. Vladimirsky. Une méthode efficace pour le contrôle optimal multi-objectifs et le contrôle optimal soumis à des contraintes intégrales. J. Comput. Math., 28(4):517–551, 2010. [4] I. Mitchell et S. Sastry. Planification de trajectoire continue avec contraintes multiples. Dans 42e Conférence internationale IEEE sur la décision et le contrôle (IEEE Cat. No.03CH37475), volume 5, pages 5502-5507, vol. 5, 2003. [5] C. M. Waespy. Une application de la programmation linéaire au contrôle optimal à consommation minimale de carburant. Rapport technique 67-16, Université de Californie, Los Angeles. NASA, juin 1967

Your Work Environment

Established in 1980, CRAN is a joint research unit (UMR 7039) run jointly by the University of Lorraine (UL) and the CNRS (INS2I Institute of Computer Science). It also hosts researchers from the Lorraine Cancer Institute (ICL, Cancer Centre), the University Hospital (CHU), and the Metz-Thionville Regional Hospital (CHR). The laboratory has around 120 lecturers and researchers, approximately 100 PhD students, post-doctoral researchers and trainees, and 33 engineers, technicians and administrative staff spread across eight sites, making a total of around 250 people. The research conducted at CRAN focuses on Control Engineering, defined as the science of modelling, analysing, controlling and monitoring dynamic systems, as well as signal processing and computer engineering. CRAN also conducts interdisciplinary research combining control engineering, signal and image processing with biology and medicine.
The lab carries out interdisciplinary work across these fields in the areas of health engineering and system reliability. These research areas cover technical systems (industrial processes, transport systems, energy generation, communication networks, etc.), environmental systems (air quality, water quality, etc.) and health (diagnosis and treatment in oncology and neurology). The outcomes of this research have both a 'societal' impact (improved safety of facilities, medical diagnostics and treatment, or environmental protection) and an economic impact (improved efficiency of facilities, medical procedures, products or services). In relation to these activities, which are broadly based on digital sciences, the laboratory is highly recognised both nationally and internationally (see the Shanghai Ranking in Automation Control). More information here: http://www.cran.univ-lorraine.fr/

Constraints and risks

The job you are applying for is located in a 'restricted access area' within the meaning of Article R 413-5-1 of the Criminal Code. Your appointment and/or posting may only take place after an access authorisation has been issued by the head of the establishment, in accordance with the provisions of Article 20-4 of Decree No. 84-431 of 6 June 1984

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

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