CENTRALE LYON - PhD thesis in System, Control and Signal Processing (2)

Project DAC Analysis and synthesis of Anomaly Detectors under Critical-time constraints

Working environment

The École Centrale de Lyon (ECL) is a public scientific, cultural and professional institution. Mmember of the Ecoles Centrales group and the Écoles Nationales d’Ingénieurs network, ECL trains high-level generalist engineers, specialized engineers, masters students and doctoral

candidates. The school hosts 2,500 engineering students and trainees, 300 master students and more than 250 doctoral students. It is characterized by recognized research supported by 6 research laboratories. 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 Automatique pour l’Ingénierie des Systèmes (AIS) 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/understanding of systems from different disciplines (electronics, electrical engineering, mechanics, biology, etc.).

In particular, expertise has been developed in the design of systems obtained by interconnecting subsystems, for which the combination of the input-output approach with (convex [BTN01, BV04]) optimization tools seems to be particularly effective. Convincing results have already

been obtained, ranging from upstream methodological contributions (e.g. [PKZS23,ACPKS23, LKD+17]) to their application to problems of strong practical interest (e.g. [PKS+21,KSCB16, GFS11]), and even to patent deposit (e.g. [PKZ+17,CGK10,CK13]). More recently, some team

members have begun to explore the topic of the safety and security of cyber-physical systems (e.g., [PCZ21b,PCZ21a,EMSZ20]).

Scientific background of the project

The challenge of system security is to ensure that the specifications are met even in the face of malicious behavior or unforeseen events. Historically divided into the fight against physical attacks and the protection of information technologies, the significant increase

in cyber-attacks against controlled systems (industrial infrastructures, power grids, drones, ...) over the last two decades [DPF+19, SRE+19] and the limitations of conventional approaches have made it necessary to develop a systemic approach to system security [SAJ15],

taking into account in particular the interaction between the cyber and physical worlds (Fig. 1).

On the one hand, traditional IT security methods focus primarily on protecting information and do not directly consider the possible physical consequences of cyber-attacks. On the other hand, classical Control and Signal Processing approaches address tolerance to independent

disturbances, but do not consider possible attacks by malicious rational actors. Thus, over the last decade, approaches have been developed to prevent, detect, and mitigate attacks on controlled systems [CST19, DPF+19].

An important issue is to find an appropriate trade-off between the desired level of security and the satisfaction of a functional specification. This is due in particular to the difficulty of assessing the risk, and especially the likelihood, of an attack due to the heterogeneity of attackers, both in terms of objectives and resources [TSSJ15].

Problem and Objectives of the thesis

In this context, the ambition of this thesis is to tackle the problem of efficient analysis and synthesis of anomaly detectors (attacks, faults) under critical-time constraint. The critical-time is the maximum time horizon for which a system is considered to be safe after the occurrence of an anomaly, i.e. the system is not in a critical state and is still able to return to a normal mode (Fig. 2). This security metric introduced in [PCZ21a] seems to be relevant at every stage of the risk management process (analysis, prevention, detection, mitigation). The underlying motivation is that an increase in critical-time gives defense mechanisms, including human operators, more time to detect and mitigate anomalies.

The performance of anomaly detectors is traditionally evaluated according to three criteria : detection rate, false alarm rate and detection delay. When synthesizing a detector, only the first two criteria are considered. The estimation of the detection delay and the verification that the system does not enter a critical state before detection (i.e. that the detection delay is less than the critical time) are then estimated in a post-synthesis phase using simulations. The first objective of this thesis is to develop an algorithmically efficient analysis method that allows to formally guarantee whether the worst-case detection delay of a given filter is less than the critical time. To achieve this, the research could build on previous work [PCZ21b,EMSZ20,BTMS17] on critical time computation and robust simulation techniques, and extend them to systems of practical interest (such as uncertain linear timevarying systems). The second objective is to propose a method able to take into account the critical-time constraint directly in the synthesis of the detection filter. An important challenge will be to obtain of an algorithmically efficient method, which may require to simplify the problem (constraints relaxation, reformulation or relevant approximation of the problem, etc.). These first two objectives take place in the context of sharp anomalies, i.e. with a severe impact on the system in a reduced amount of time. The third objective will be to synthesize an anomaly detector in order to guarantee a minimum critical-time for the so-called stealthy attacks, i.e. attacks designed not to be detected by the filter. As the expected contributions are mainly methodological, the results will be valorized mainly through presentations at international conferences and publications in leading journals in the field of Control and System theory.

Références

[ACPKS23] J. Ayala-Cuevas, A. Perodou, A. Korniienko, and G. Scorletti. A frequency-domain Integral Quadratic Constraint approach to the analysis of Harmonically TimeVarying Systems. Automatica, 152 :110956, 2023. [BTMS17] H. Ben-Talha, P. Massioni, and G. Scorletti. Robust Simulation of ContinuousTime Systems with Rational Dynamics. International Journal of Robust and Nonlinear Control, 27(16) :3097–3108, 2017. [BTN01] A. Ben-Tal and A. Nemirovski. Lectures on Modern Convex Optimization : Analysis, Algorithms, and Engineering Applications. Society for Industrial and Applied Mathematics, 2001. [BV04] S. P. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004. [CGK10] E. Colinet, D. Galayko, and A. Korniienko. Device for generating clock signals for asymmetric comparison of phase, 2010. United States Patent WO/2011/051407 (PCT/EP2010/066405). [CK13] E. Colinet and A. Korniienko. Device and method for compensating a signal propagation delay, 2013. US Patent 8,373,476. [CST19] M. S. Chong, H. Sandberg, and A. M. H. Teixeira. A Tutorial Introduction to Security and Privacy for Cyber-Physical Systems. In 2019 18th European Control Conference (ECC), pages 968–978, 2019. [DPF+19] S. M. Dibaji, M. Pirani, D. B. Flamholz, A. M. Annaswamy, K. H. Johansson, and A. Chakrabortty. A Systems and Control Perspective of CPS security. Annual Reviews in Control, 47 :394–411, 2019. [EMSZ20] C. Escudero, P. Massioni, G. Scorletti, and E. Zamaï. Security of Control Systems : Prevention of Aging Attacks by means of Convex Robust Simulation Forecasts. IFAC-PapersOnLine, 53(2) :4452–4459, 2020. [GFS11] A. Goelzer, V. Fromion, and G. Scorletti. Cell Design in Bacteria as a Convex Optimization Problem. Automatica, 47(6) :1210–1218, 2011. [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, 26 :3–27, 01 2016. [LKD+17] K. Laib, A. Korniienko, M. Dinh, G. Scorletti, and F. Morel. Hierarchical Robust Performance Analysis of Uncertain Large Scale Systems. IEEE Transactions on Automatic Control, 63(7) :2075–2090, 2017. [PCZ21a] A. Perodou, C. Combastel, and A. Zolghadri. Critical-Time Analysis of CyberPhysical Systems subject to Actuator Attacks and Faults. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 4188–4193, Dec. 2021. [PCZ21b] A. Perodou, C. Combastel, and A. Zolghadri. Towards Anomaly-Tolerant Systems by Dissipation Block Synthesis. In 2021 5th International Conference on Control and Fault-Tolerant Systems (SysTol), pages 19–24, Sept. 2021. [PKS+21] A. Perodou, A. Korniienko, G. Scorletti, M. Zarudniev, J. B. David, and I. O’Connor. Frequency Design of Lossless Passive Electronic Filters : A State-Space Formulation of the Direct Synthesis Approach. IEEE Transactions on Circuits and Systems I : Regular Papers, 68(1) :161–174, 2021.

[PKZ+17] M. Pelissier, A. Korniienko, M. Zarudniev, G. Scorletti, O. Mokrenko, E. Blanco, P. Villard, and G. Billiot. Phase-locked loop with multiple degrees of freedom and its design and fabrication method, March 2017. US Patent 9,602,114. [PKZS23] A. Perodou, A. Korniienko, M. Zarudniev, and G. Scorletti. Frequency Synthesis of Interconnected Homogeneous LTI Systems. IEEE Transactions on Automatic Control, 2023. [SAJ15] H. Sandberg, S. Amin, and K. H. Johansson. Cyberphysical Security in Networked Control Systems : An Introduction to the Issue. IEEE Control Systems Magazine, 35(1) :20–23, 2015. [SRE+19] H. S. Sánchez, D. Rotondo, T. Escobet, V. Puig, and J. Quevedo. Bibliographical Review on Cyber Attacks from a Control Oriented Perspective. Annual Reviews in Control, 48 :103–128, 2019. [TSSJ15] A. Teixeira, K. C. Sou, H. Sandberg, and K. H. Johansson. Secure Control Systems : A Quantitative Risk Management Approach. IEEE Control Systems Magazine, 35(1) :24–45, 2015. [ZB15] Q. Zhu and T. Basar. Game-Theoretic Methods for Robustness, Security, and Resilience of Cyberphysical Control Systems : Games-in-Games Principle for Optimal Cross-Layer Resilient Control Systems. IEEE Control Systems Magazine, 35(1) :46–65, 2015

Requirements

Candidate profile

We are looking for candidates with a master’s degree in System and Control or Signal Processing (MSc or MEng) and an excellent academic record. Those with a general degree and strong skills in applied mathematics are also encouraged to apply. Interest in developing optimization-based methods and experience with Matlab are also valued.