USP-Cofecub Control of Dynamic Systems Subject to Stochastic Jumps and Inria Associate Team CDSS (2013-2016) ↑
Leaders F. Dufour (Inst. Polytech. Bordeaux and Inria), O. Costa (Univ. São Paulo)
Participants B. de Saporta, F. Dufour, P. Rouchon (France), E. Costa, O. Costa, P. Pereira da Silva (Brazil)
The main goals of this joint cooperation is to study the control of dynamic systems subject to stochastic jumps. In my topic, we focus on numerical methods for solving control and filtering problems related to Markov jump linear systems. This project allows a first cooperation between with Eduardo F. Costa (Univ. São Paulo à São Carlos, Brazil).CDSS website
PROMMECE (2016-2019) ↑
Leader B. de Saporta
Participants B. Cloez (INRA), M. Joubaud (Univ. Montpellier), K. Milferstedt (INRA), M. Ribatet (Univ. Montpellier), JP. Steyer (INRA)
The purpose of project PROMMECE is to study new mathematical models to describe the evolution of cell populations over time. Typically, these cells grow and divide into two daughter cells that will in turn grow and divide. Although cells descending from the same initial ancestor cell are genetically identical, there is a variability in measured quantities between cells (growth rate, concentration of a given protein, ...). It is therefore necessary to include randomness in models describing these phenomena. This project focuses on two main issues. The first one is to determine if there is asymmetry and memory in cell division. To do this, we will compare the existing deterministic models with new stochastic models to find experimental criteria for discriminating between models with and without memory. The second one concerns simulation and control of cell populations: how to dynamically adjust at best various parameters that influence cell growth (amount of nutrient, temperature, amount of biomass withdrawn ...) to achieve a predetermined goal such as optimizing the production of biogas.
ANR Piece (2013-2017) ↑
Leader F. Malrieu (Univ Tours)
Participants J.-B. Bardet (Univ. Rouen), B. Cloez (Univ. Toulouse), B. de Saporta (Univ. Bordeaux), M. Doumic (INRIA Rocquencourt), N. Krell (Univ. Rennes 1), A. Genadot (Univ. Pierre et Marie Curie), D. Goreac (Univ. Paris-Est-Marne-La-Vallée), F. Malrieu (Univ. Tours), P. Robert (INRIA Rocquencourt), G. Wainrib (Univ. Paris 13), P.-A. Zitt (Univ. Paris-Est-Marne-la-Vallée)
The scientific leader of ANR Jeunes chercheuses et jeunes chercheurs Piece is Florent Malrieu (Univ Tours). I am in charge of task 3 (simulation and estimation). Piecewise Deterministic Markov Processes (PDMP) are non-diffusive stochastic processes which naturally appear in many areas of applications as communication networks, neuron activities, biological populations or reliability of complex systems. Their mathematical study has been intensively carried out in the past two decades but many challenging problems remain completely open. This project aims at federating a group of experts with different backgrounds (probability, statistics, analysis, partial derivative equations, modelling) in order to pool everyone's knowledge and create new tools to study PDMPs. The main lines of the project relate to estimation, simulation and asymptotic behaviors (long time, large populations, multi-scale problems) in the various contexts of application.
ANR FauToCoES (2009-2013) ↑
Leader F. Dufour (Inst. Polytech. Bordeaux et Inria)
Participants R. Azaïs, A. Brandejsky, M. Colin, T. Colin, B. de Saporta, F. Dufour, A. Gégout-Petit (Inria CQFD et MC2), M. Puiggali, M. Touzet (Labo de Mécanique Physique, Univ. Bordeaux), F. Boyer, F. Hubert (Univ. Provence), C. Elegbede, M. Euzen (Astrium)
The scientific leader of ANR Fautocoes is François Dufour (équipe CQFD, Inria Bordeaux Sud Ouest). I am in charge of task 3 (stochastic control). Our aim is to use the framework of piecewise deterministic Markov processes (PDMPs) with an emphasis on probabilistic and deterministic numerical methods: to model complex physical systems and phenomena; to compute expectations of functionals of the process in order to evaluate the performance of the system; to develop theoretical and numerical control tools for PDMPs to optimize the performance and/or to maintain system function when a failure has occurred.
Thales Optronique (2014-2017) ↑
Participants B. de Saporta, F. Dufour, A. Geeraert (Inria), C. Baysse, D. Bihannic, M. Prenat (Thales)
Type Funding of the PhD thesis of A. Geeraert and support contract.
We will develop new powerful numerical methods to optimize the disponibility of Thales equipments. The aim is to go from a corrective maintenance to a predictive one. We propose a method that is both numerically efficient and mathematically sound to solve long term optimization problems with sequential decision making regarding the dates and types of intervention to be performed.
Airbus Defence & Space (2013-2016) ↑
Participants B. de Saporta, F. Dufour, C. Nivot (Inria), J. Behar, D. Berard-Bergery, C. Elegbede (Airbus DS)
Type Co-funding of the internship and PhD thesis of C. Nivot and support contract within a Région Aquitaine grant.
he goal of this project is the optimization of the assembly line of the future European launcher, taking into account several kinds of economical and technical constraints. We have started with a simplified model with five components to be assembled in workshops liable to breakdowns. We have modeled the problem using the Markov Decision Processes (MDP) framework and built a simulator of the process in order to run an optimization procedure.
DCNS (2010-2014) ↑
Participants B. de Saporta, F. Dufour, H. Zhang (Inria), D. Laneuville, A. Nègre (DCNS)
Type Industrial research contract (renewed every year).
he increasing complexity of warfare submarine missions and crew reduction has led DCNS to study new tactical help functions for underwater combat management systems. In this context, the objective is to find optimal trajectories according to the current mission type by taking into account sensors, environment and surrounding targets. We modeled the problem as a Markov Decision Process first taking into account a single target vessel and allowing only to control the immersion of the submarine. In 2011, we extended our previous results to multiple target vessels. In 2012, we dealt with multiple target vessels and 3D control. In 2013, we also coupled our code with the output of a tracking software to take more realistically into account the uncertainty on the position and speed of the targets.
Thales Optronique (2010-2013) ↑
Participants C. Baysse, B. de Saporta, A. Gégout-Petit, J. Saracco (Inria), D. Bihannic, M. Prenat (Thales)
Type Funding of the PhD thesis of C. Baysse (supervised by A. Gégout-Petit and J. Saracco) and support contract.
he goal of the project is the optimization of the maintenance of a on board system with a HUMS (Health Unit Monitoring Systems). We have proposed a hidden Markov model to detect as soon as possible a possibly degraded state for an optronic equipment. The detection procedure is based on on-line recordings performed by the HUMS. We then proposed an optimal and dynamic maintenance policy, adapted to the state of the system and taking into account both random failures and those related to the degradation phenomenon, based on a PDMP model.
EDF (2010-2012) ↑
Participants B. de Saporta, F. Dufour, H. Zhang (Inria), G. Deleuze (EDF), J.F. Aubry, G. Babykina, N. Brinzei, S. Medjaher (CRAN, Univ. Lorraine), A. Barros, C. Berenguer, A. Grall, Y. Langeron, D.N. Nguyen (Univ. Technologie Troyes)
Type Industrial research contract within the GIS S3S (Supervision and Safety of Complex Systems).
The objective of this project is develop new methodologies for studying the dynamic reliability of controlled systems used in the critical area of power generation and process industries. We worked on a benchmark of steam generator with four physical variables: feedwater flowrate , steam flow, narrow range water level and wide range water level. A PID controller is used to maintain the water level within limits of set-points. The system is composed of seven components: 1 passive system representing vapor transport system, 3 extraction pumps, 2 feeding turbopumps, and 1 waterflow regulation valve. We implemented a simulator of this hybrid process based on a PDMP model and computed failure probabilities for a typical 18-month scenario.
Astrium Space Transportation (2008-2013) ↑
Participants A. Brandejsky, B. de Saporta, F. Dufour, H; Zhang (Inria), C. Elegbede (Astrium)
Type Funding of the PhD thesis of A. Brandejsky and support contract within ANR Fautocoes.
The initial goal of this project was to propose new random models for fatigue of structure, to study an approach to evaluate the probability of occurrence of events defined by the crossing of a threshold and to propose numerical methods for the optimization of maintenance policies. We used Piecewise Deterministic Markov Processes (PDMPs) to model the randomness of the fatigue life of the material and the succession of the different loading regimes. This class of models allows us to input a propagation law adapted to the current regime of the propagation (usually called stage II and stage III in the literature) and also adapted to the current cycle (storage, transport, takeoff, etc.). The proposed approach allows us to make prediction about time of transition to the breaking regime. We proposed a new probabilistic approach to compute expectations of PDMPs based on quantization techniques. We have obtained general results to simulate a general functional of the PDMP. The same ideas have been used to compute approximations of the law and moments of exit times for general PDMPs. Astrium has provided an industrial example to test our numerical optimization tools on. It concerns a metallic structure subject to corrosion that is stored for potentially long times in different more or less stressing environments. We computed the service time of the structure, that is the law of the exit time for the corrosion level to reach a given threshold. We also proposed an optimized maintenance policy for this structure that is dynamic and adapted to the specific history of each structure.
Astrium Space Transportation (2008-2009) ↑
Participants R. Azaïs, B. de Saporta, F. Dufour, A. Gégout-Petit, H. Zhang (Inria), M. Touzet (I2M, Univ. Bordeaux), C. Elegbede (Astrium ST)
Type Industrial research contract.
The goal of this two-year project is to study random models for crack proagation.
Working with Huilong Zhang on the DCNS grant
