Description du sujet de thèse

Project SystHeI - Towards efficient analysis and synthesis of Heterogeneous Interconnected Systems: application to signal estimation

Keywords : System and Control Theory - Signal Processing - Interconnected dynamical systems - Estimation filters – Applied Mathematics - Convex Optimization

The ongoing integration of information technologies into engineering systems is radically changing the possibilities in a wide range of applications (energy production and distribution, telecommunications, transportation of goods and people, Industry 4.0, medicine, intelligent buildings, etc.), but at the cost of a drastic increase in the complexity of the associated design problems. In addition to having to meet ever more stringent and even new requirements (performance, safety, security, energy efficiency, cost, etc.), it must explicitly take into account the complexity of the interconnection (large size, degraded communication, live-machine interface, etc.) of intrinsically complex and heterogeneous systems. To meet these challenges, traditional design methods based on simulation and a trial-and-error approach often appear to be limited, and it has become necessary to develop adapted methods based on (convex) optimization that enable efficient design.

In this context, the goal of this thesis is to address the problem of efficient analysis and synthesis of interconnected heterogeneous systems. This problem is particularly relevant for large-scale systems (e.g., energy distribution networks, sensor networks, gene regulation networks, etc.).

A first strategy to tackle this problem is to consider the global system and use classical methods of analysis and synthesis. However, in the case of large systems, this type of approach will generally lead to very large optimization problems. A second strategy is to describe the overall system as a collection of subsystems, modeled by a characterization on the input and output signals of each subsystem. This type of approach has the advantage of greatly reducing the complexity of the optimization problems. In addition, for an application of estimation filter synthesis, this idea makes it possible to reduce the order of the filters obtained. This second strategy has recently led to significant results in the special case of homogeneous subsystems, i.e., those represented by the same model (see, for example, [ACPKS23, PKZS23, KSCB16]). However, in the more general case of heterogeneous subsystems, this approach tends to be conservative, i.e. it does not necessarily allow to find a solution even if one exists. The main suspected cause of this pessimism is the input-output characterization performed for each subsystem independently of the others, which implicitly assumes that the subsystems are independent and therefore that their models have no similarities.

The objective of this thesis is to overcome this problem by exploring an original idea: introducing dependence between subsystem characterizations to take into account similarities (e.g. algebraic or topological) in their modeling. The goal is to improve the trade-off between algorithmic complexity and conservatism by finding a balance between the two strategies described above. The interest and limitations of this idea will be illustrated in particular by a signal estimation filter synthesis application.

For more details, see p.5 of www.ampere-lab.fr/IMG/pdf/1_sujet_systhei.pdf

[ACPKS23] J. Ayala-Cuevas, A. Perodou, A. Korniienko, and G. Scorletti. A frequency-domain Integral Quadratic Constraint approach to the analysis of Harmonically Time-Varying Systems. Automatica, 2023.
[PKZS23] A. Perodou, A. Korniienko, M. Zarudniev, and G. Scorletti. Frequency Synthesis of Interconnected Homogeneous LTI Systems. IEEE Transactions on Automatic Control, 2023.
[KSCB16] A. Korniienko, G. Scorletti, E. Colinet, and E. Blanco. Performance Control for Interconnection of Identical Systems : Application to PLL network design. International Journal of Robust and Nonlinear Control, 2016.

Contexte de travail

The École Centrale de Lyon (ECL) is a public scientific, cultural and professional institution. ECL's research activities are directed to and for the business world through numerous industrial contracts.

The Ampère-lab is a joint research unit (CNRS, Ecole Centrale de Lyon, INSA Lyon, Université Lyon 1) of more than 150 researchers based in Lyon, France, working on the rational use of energy in systems in relation to their environment. The research carried out by the System Engineering department includes the development of methods and tools for optimizing and controlling the dynamic behavior of systems in a wide range of application domains, in collaboration with other departments of the laboratory and other engineering laboratories. The combination of theoretical and applied dimensions of this research constitutes its great originality.

Over the last few years, the advisors have been working on the possibilities offered by Systems, Control and Signal approaches for the development of methods for the design and understanding of systems from different disciplines (electronics, electrical engineering, mechanics, biology, etc.). In particular, an expertise has been developed in the design of systems obtained by interconnecting subsystems, for which the combination of the input-output approach with convex optimization tools seems to be particularly effective. Convincing results have already been obtained, ranging from upstream methodological contributions to their application to problems of strong practical interest and even to patent deposit.

Le poste se situe dans un secteur relevant de la protection du potentiel scientifique et technique (PPST), et nécessite donc, conformément à la réglementation, que votre arrivée soit autorisée par l'autorité compétente du MESR.

Contraintes et risques

Risks : nothing.
Constraint : Laboratory in ZRR, FSD notification required. The position is located in an area covered by the protection of scientific and technical potential (PPST), and therefore requires, in accordance with regulations, that your arrival be authorized by the competent MESR authority.
See pdf subject for more information.

Do not hesitate to contact the advisors team directly for further details (contact in pdf subjects).