Pauline Bernard

Lecturer

Center · CAS

Keywords

Awards & distinctions

2019 European PhD Award on Control for Complex and Heterogeneous Systems

Team

CAS

Biography

Pauline Bernard is a researcher specializing in observation and state estimation for dynamic systems, with particular expertise in hybrid, nonlinear, and discrete-time systems. Her work focuses in particular on the design of observers for systems subject to unknown or poorly detected state jumps, combining theoretical approaches such as KKL (Kazantzis-Kravaris/Luenberger) observers, high-gain methods, or techniques based on linear matrix inequalities (LMIs). She also explores the extension of these methods to contexts where classical assumptions of observability or distinguishability are not satisfied, proposing innovative solutions such as set-valued observers or sliding transformations. Her research applies to a variety of fields, ranging from mechanical systems to electrical machines and hybrid neural models, illustrating a unifying approach between theory and practical applications.

Publication(s)

2026
Dealing with Indistinguishability in Gluing KKL Observer Design for Hybrid Systems with Unknown Jump Times DOI : 10.1109/TAC.2026.3689008
2026
Observer design for hybrid systems with partially affine forms and known jump times: Applications to walking robots DOI : 10.1016/j.automatica.2026.113043
2025
Saltation-Based analysis of estimation error in observers for hybrid systems with unknown jump times DOI : 10.1109/CDC57313.2025.11312843
2024
On a Benchmark in Output Regulation of Non-Minimum Phase Systems DOI : 10.1016/j.ifacol.2024.10.147
2024
Towards Gluing KKL Observer for Hybrid Systems with Unknown Jump Times DOI : 10.1109/CDC56724.2024.10886607
2024
Arbitrarily Fast Robust KKL Observer for Nonlinear Time-Varying Discrete Systems DOI : 10.1109/TAC.2023.3328833
2024
On the existence of KKL observers with nonlinear contracting dynamics DOI : 10.1016/j.ifacol.2024.10.223
2024
Constructible Canonical Form and High-gain Observer in Discrete Time DOI : 10.1109/CDC56724.2024.10885959
2024
Reconstructing indistinguishable solutions via a set-valued KKL observer DOI : 10.1016/j.automatica.2024.111703
2024
Semiglobal High-Gain Hybrid Observer for a Class of Hybrid Dynamical Systems With Unknown Jump Times DOI : 10.1109/TAC.2024.3355324
2024
Observer Design for Hybrid Systems with Linear Maps and Known Jump Times DOI : 10.1007/978-3-031-49555-7_6
2023
Further remarks on KKL observers DOI : 10.1016/j.sysconle.2022.105429
2023
Coupling Flow and Jump Observers for Hybrid Systems with Known Jump Times DOI : 10.1016/j.ifacol.2023.10.522
2023
Kalman-like Observer for Hybrid Systems with Linear Maps and Known Jump Times DOI : 10.1109/CDC49753.2023.10383629
2023
Robust Sensorless Flux and Position Estimation for SynRMs DOI : 10.1109/IECON51785.2023.10312356
2023
KKL set-valued observers for non-observable systems DOI : 10.1016/j.ifacol.2023.02.013
2022
Observer Design based on Observability Decomposition for Hybrid Systems with Linear Maps and Known Jump Times DOI : 10.1109/CDC51059.2022.9993225
2022
Observer design for hybrid dynamical systems with approximately known jump times DOI : 10.1016/j.automatica.2022.110225
2022
KKL observer design for sensorless induction motors DOI : 10.1109/CDC51059.2022.9992800
2022
Constrained State Estimation for Nonlinear Systems: A Redesign Approach Based on Convexity DOI : 10.1109/TAC.2021.3064537
2022
On the existence of robust functional KKL observers DOI : 10.23919/ACC53348.2022.9867611
2022
Observer design for continuous-time dynamical systems DOI : 10.1016/j.arcontrol.2021.11.002
2022
A Novel Observer for Induction Motors, with an Application to Soft Starters DOI : 10.1109/ICEM51905.2022.9910680
2021
Estimation of Position and Resistance of a Sensorless PMSM: A Nonlinear Luenberger Approach for a Nonobservable System DOI : 10.1109/TAC.2020.2981341
2021
Observer design via interconnections of second-order mixed sliding-mode/linear differentiators DOI : 10.1002/rnc.5301
2021
Avalanche Victim Search via Robust Observers DOI : 10.1109/TCST.2020.3016665
2021
On the Semi-Global Stability of an EK-Like Filter DOI : 10.1109/LCSYS.2020.3044030
2021
Approximate Nonlinear Regulation via Identification-Based Adaptive Internal Models DOI : 10.1109/TAC.2020.3020563
2021
Hybrid Systems with Continuous-time Inputs: Subtleties in Solution Concepts and Existence Results DOI : 10.1109/CDC45484.2021.9683389
2021
Remarks about the numerical inversion of injective nonlinear maps DOI : 10.1109/CDC45484.2021.9683097
2021
A Local Hybrid Observer for a Class of Hybrid Dynamical Systems with Linear Maps and Unknown Jump Times DOI : 10.1109/CDC45484.2021.9682924
2021
Robust Frequency Estimation of Multi-Harmonic Signals DOI : 10.23919/ECC54610.2021.9654931
2020
Robust sensorless estimation of the position and magnet flux of PMSMs DOI : 10.1109/IECON43393.2020.9254486
2020
Numerical design of Luenberger observers for nonlinear systems DOI : 10.1109/CDC42340.2020.9304163
2020
Avalanche victim search via robust observers DOI : 10.1109/ICRA40945.2020.9196646
2020
On Notions of Detectability and Observers for Hybrid Systems DOI : 10.1109/CDC42340.2020.9304274
2020
Higher-order singular perturbations for control design with application to the control of induction motors DOI : 10.1109/CDC42340.2020.9304011
2020
Hybrid dynamical systems with hybrid inputs: Definition of solutions and applications to interconnections DOI : 10.1002/rnc.4756
2020
Adaptive output regulation via nonlinear Luenberger observer-based internal models and continuous-time identifiers DOI : 10.1016/j.automatica.2020.109261
2020
Mixing sliding mode and linear differentiators for 2nd and 3rd order systems DOI : 10.1016/j.ifacol.2020.12.1123
2020
Hybrid implementation of observers in plant's coordinates with a finite number of approximate inversions and global convergence DOI : 10.1016/j.automatica.2019.108654
2019
An algorithm to generate solutions to hybrid dynamical systems with inputs DOI : 10.23919/acc.2019.8815141
2019
Redesign of discrete-time nonlinear observers with state estimate constrained in prescribed convex set DOI : 10.1016/j.ifacol.2019.12.003
2019
Adaptive output regulation via nonlinear Luenberger observers DOI : 10.1016/j.ifacol.2019.12.024
2019
Hybrid implementation of observers in initial coordinates with a finite number of approximate inversions and global convergence DOI : 10.23919/acc.2019.8815160
2019
Observer Design for Nonlinear Systems DOI : 10.1007/978-3-030-11146-5_11
2018
Observers for Hybrid Dynamical Systems with Linear Maps and Known Jump Times DOI : 10.1109/CDC.2018.8618937
2018
Expressing an observer in preferred coordinates by transforming an injective immersion into a surjective diffeomorphism DOI : 10.1137/15M1037755
2018
Convergence of gradient observer for rotor position and magnet flux estimation of permanent magnet synchronous motors DOI : 10.1016/j.automatica.2018.04.009
2017
On the triangular canonical form for uniformly observable controlled systems DOI : 10.1016/j.automatica.2017.07.034
2017
Observers for a non-Lipschitz triangular form DOI : 10.1016/j.automatica.2017.04.054
2017
Robustness of rotor position observer for permanent magnet synchronous motors with unknown magnet flux DOI : 10.1016/j.ifacol.2017.08.1866
2017
Luenberger observers for nonlinear controlled systems DOI : 10.1109/CDC.2017.8264200
2016
Non Lipschitz triangular canonical form for uniformly observable controlled systems DOI : 10.1016/j.ifacol.2016.10.214
2015
Tools for observers based on coordinate augmentation DOI : 10.1109/CDC.2015.7403215
2014
Adaptive output-feedback stabilization of non-local hyperbolic PDEs DOI : 10.3182/20140824-6-za-1003.00108
2014
Adaptive output-feedback stabilization of non-local hyperbolic PDEs DOI : 10.1016/j.automatica.2014.09.001

Projects

2024-2028 Observer design for nonsmooth and hybrid systems Lead Investigator

Teaching

Control Theory (Course)

Course Director

Differential, Integral, and Stochastic Calculus I (Math1)

Course Director

This first module of UE11 will begin with an introduction to the topology of metric spaces: open sets, closed sets, density, completeness, compactness, and the space of continuous maps between metric spaces. We will then cover the essential elements of measure theory (without doing all the proofs in lecture), which allows us to define the Lebesgue integral; we will clarify how it differs from the Riemann integral covered in preparatory classes. This integral will allow us to define the main functional spaces used in the mathematical study of equations in physics—the Lp spaces—and in particular the L2 space. We will then study Hilbert spaces (of which L2 is an archetypal example), which are generalizations of Euclidean spaces to infinite dimensions, and we will examine their main properties, in particular the existence of so-called Hilbert bases. The final part of the course will be devoted to differential calculus for mappings from Rn to Rm: the concept of a partial derivative, the differential of a mapping, the finite increase theorem in Rd, the implicit function theorem, and the local inversion theorem. Advanced tutorial sessions will allow motivated students to go beyond the concepts required for the exam: more in-depth analysis of measure and integration theory, functional analysis, Banach spaces, the Hahn-Banach theorem, operators in infinite-dimensional spaces, Sobolev spaces… This theoretical course aims to provide the foundations that will enable students to tackle the major challenges of applied mathematics, in particular the study and numerical solution of differential equations, partial differential equations, and optimization.

Differential, Integral, and Stochastic Calculus II (Math2)

Course Director

EC2 consists of two modules: Differential Equations and Probability. The differential equations course aims to introduce students to the study of dynamical systems: existence, uniqueness, and regularity of solutions to a differential equation (Peano–Arzela, Cauchy-Lipschitz, regularity with respect to initial conditions in finite time, chaotic systems), as well as an introduction to the study of the asymptotic behavior of solutions (periodic cycles, asymptotic stability of equilibrium points, etc.) An introduction to the simulation and numerical analysis of differential equations is also provided (discretization schemes, consistency/convergence analysis, differences between explicit and implicit schemes for stiff systems, the role of symplectic schemes for Hamiltonian systems, etc.) The probability course aims to consolidate and supplement the knowledge of probability theory acquired in CPGE, but above all to develop probabilistic reasoning. In CPGE, probability was studied in the context of random phenomena with at most a countable number of possible outcomes. Probabilities defined on the real line, as well as real random variables and vectors, are first introduced within the general formalism of measure theory—covered in EC1—which allows for the inclusion of the discrete case. The concepts of independence and conditioning of random variables, sequences of random variables, and finally stochastic simulation methods are addressed in turn to cover all the prerequisites necessary for the various engineering specializations offered at the school, particularly data science.

Control Theory (Research Quarter)

Course Director

This quarter offers an introduction to research in control theory (Automation), a discipline within the field of mathematics applied to physical systems. To begin, a week of theoretical lectures introduces the essential elements of control theory and classical proof techniques and methods (stabilization, controllability, observability). These concepts are illustrated through concrete engineering examples that help students understand the role of feedback in real-world systems (mechanical, chemical, electrical, aerospace, mechatronic, automotive, oil, and energy systems, among others). Students then work on research topics proposed and supervised by faculty members at the Center for Automation and Systems at Mines Paris - PSL. Students enrolled in this quarter learn to apply these theoretical concepts mathematically, illustrate them with practical examples, and communicate the results of their work in accordance with academic standards. Students participate in laboratory activities and, in particular, attend seminars with researchers.

PhD supervision

2024 Anti-windup management for electric motors by electrical limitations WEHBE Ali
2024 State observation for non-regular and hybrid dynamic systems ALLEAUME Valentin
2021 Observer Synthesis for Hybrid Systems TRAN Gia Quoc Bao