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1. Design of a Fractional Pseudo-Chaotic Random Number Generator

Author

Chunxiao Yang, Ina Taralova, Jean Jacques Loiseau, Safwan El-Assad, École Centrale de Nantes (ECN), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Institut d'Électronique et des Technologies du numéRique (IETR), Université de Nantes (UN)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Commande (Commande), PSI (PSI), Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES), Ecole Polytechnique de l'Université de Nantes (EPUN), Université de Nantes (UN), Nantes Université (NU)-Université de Rennes 1 (UR1), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Commande (LS2N - équipe Commande), PSI (LS2N - équipe PSI), Université de Nantes (UN)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Discretization, 020208 electrical & electronic engineering, Chaotic, 02 engineering and technology, Lyapunov exponent, Grid, Nonlinear Sciences::Chaotic Dynamics, symbols.namesake, [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], 020901 industrial engineering & automation, 0202 electrical engineering, electronic engineering, information engineering, Piecewise, symbols, Applied mathematics, Cryptosystem, [INFO]Computer Science [cs], [NLIN]Nonlinear Sciences [physics], Stream cipher, Mathematics, Generator (mathematics)
Abstract

International audience; In this paper, we design a pseudo-chaotic random number generator using fractional chaotic systems. A non-uniform grid calculation method is proposed and employed to numerically solve the fractional systems by introducing a skew-tent map to vary the step size of the grid. Greater chaoticity in terms of Lyapunov exponent has been achieved by applying the proposed approach to the solution calculation of the fractional chaotic Chen's and Lu's systems. By adopting the piecewise constant argument method, one 1D fractional generalized double-humped logistic system (FGDHL) is discretized. A fractional pseudo-chaotic random number generator (FPCRNG) has been proposed by performing XOR (exclusive-or) operations to the states of the fractional Chen's system, fractional Lu's system, and the FGDHL systems. The security analysis of the generator and the statistical experiment of a stream cipher implementing the proposed FPCRNG prove that the proposed structure is efficient and can be used in the cryptosystem design.

Published
2020
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2. Modelling and control of multi-energy systems through multi-prosumer node and economic model predictive control

Author

Fabien Claveau, Pierrick Haurant, Philippe Chevrel, Bruno Lacarrière, Pierre Clément Blaud, Anthony Mouraud, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Commande (LS2N - équipe Commande), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Automatique, Productique et Informatique (IMT Atlantique - DAPI), IMT Atlantique (IMT Atlantique), Département Systèmes Energétiques et Environnement (IMT Atlantique - DSEE), Optimisation - Système - Energie (GEPEA-OSE), Laboratoire de génie des procédés - environnement - agroalimentaire (GEPEA), Institut Universitaire de Technologie - Nantes (IUT Nantes), Université de Nantes (UN)-Université de Nantes (UN)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-Institut Universitaire de Technologie Saint-Nazaire (IUT Saint-Nazaire), Université de Nantes (UN)-Ecole Polytechnique de l'Université de Nantes (EPUN), Université de Nantes (UN)-École nationale vétérinaire, agroalimentaire et de l'alimentation Nantes-Atlantique (ONIRIS)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Universitaire de Technologie - La Roche-sur-Yon (IUT La Roche-sur-Yon), Université de Nantes (UN)-Institut Universitaire de Technologie - Nantes (IUT Nantes), Université de Nantes (UN), CEA Tech en régions (CEA-TECH-Reg), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Conseil Régional des Pays de la Loire, Commande (Commande), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Université de Nantes (UN)-Université de Nantes (UN)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Ecole Polytechnique de l'Université de Nantes (EPUN), Université de Nantes (UN)-Université de Nantes (UN)-Institut Universitaire de Technologie - Nantes (IUT Nantes), Université de Nantes (UN)-Institut Universitaire de Technologie Saint-Nazaire (IUT Saint-Nazaire), Université de Nantes (UN)-Institut Universitaire de Technologie - La Roche-sur-Yon (IUT La Roche-sur-Yon), Université de Nantes (UN)-Ecole Nationale Vétérinaire, Agroalimentaire et de l'alimentation Nantes-Atlantique (ONIRIS)-Université Bretagne Loire (UBL)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Ecole Nationale Vétérinaire, Agroalimentaire et de l'alimentation Nantes-Atlantique (ONIRIS)-Université Bretagne Loire (UBL)

Subjects
Computer science, 020209 energy, media_common.quotation_subject, Economic Model Predictive Control, Energy Engineering and Power Technology, 02 engineering and technology, 7. Clean energy, Adaptability, Multi-Prosumer Node, Economic cost, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Energy transformation, Electrical and Electronic Engineering, media_common, Energy carrier, Energy Hub, business.industry, 020208 electrical & electronic engineering, Converters, Reliability engineering, Renewable energy, Model predictive control, Multi-Energy System, [SPI.MECA.THER]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Thermics [physics.class-ph], Grid energy storage, business
Abstract

International audience; The present study deals with Multi-Energy Systems (MES) modelling and advanced control with Economic Model Predictive Control (EMPC). MES provide energy flexibility, efficiency, and adaptability thanks to several energy carriers. MES are identified as a lever for integrating renewable energy. A MES novel formulation technique called Multi-Prosumer Node (MPN) is developed in this paper. MPN makes possible the modeling of MES, considering MES dynamics , several energy carriers, converters, on-grid, and off-grid. In addition, this MES modeling approach is compatible with predictive control strategies like the EMPC. In fact, EMPC is able to take into account loads, weather, renewable power and energy grid cost predictions to minimise economic costs. A real case study is implemented to examine MPN capabilities, which it is composed of renewable generators, loads, storages from two-energy carriers. Two real scenarios have been developed in order to represent realistic winter and summer cases. Simulation results, thanks to modelling with MPN and EMPC advanced control, demonstrate that the node is optimally controlled, devices dynamics are considered on a minute scale, and energy conversion from one carrier to another one is taken into account while economic cost minimisation is performed. The gained results indicate that the presented MPN modelling and optimisation approach reduces economic cost by 8.21% in winter case and 84.24% in summer case compared to the benchmarks which are composed of rule-based control.

Published
2020
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3. A robust pseudo-chaotic number generator for cryptosystem based on chaotic maps and multiplexing mechanism

Author

Ina Taralova, Safwan El Assad, Zongchao Qiao, Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Commande (LS2N - équipe Commande), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut d'Électronique et des Technologies du numéRique (IETR), Université de Nantes (UN)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Commande (Commande), Nantes Université (NU)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Université de Rennes 1 (UR1), and Université de Rennes (UNIV-RENNES)

Subjects
[SPI.OTHER]Engineering Sciences [physics]/Other, 021110 strategic, defence & security studies, Security analysis, Number generator, Computer science, 0211 other engineering and technologies, Chaotic, 020206 networking & telecommunications, 02 engineering and technology, discrete chaotic maps, Topology, Multiplexing, pseudo-chaotic number generator, [SPI]Engineering Sciences [physics], Finite field, 0202 electrical engineering, electronic engineering, information engineering, multiplexing mechanism, Cryptosystem, finite field, Mechanism (sociology), ComputingMilieux_MISCELLANEOUS, security analysis
Abstract

International audience

Published
2019

4. Circuit realization of a hybrid delay chaotic secure communication system over a noisy receiver

Author

Malek Ghanes, K. Kemih, J-P. Barbot, H. Kenouni, Laboratoire d'Electrotechnique et d'Electronique Industrielle, L2EI, [Université Jilel] (L2EI), Université Mohammed Seddik Benyahia [Jijel] | University of Jijel (UMSBJ), Commande (LS2N - équipe Commande), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Non-Asymptotic estimation for online systems (NON-A-POST), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Mohamed seddik Ben Yahia [Jijel], Commande (Commande), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique)

Subjects
0209 industrial biotechnology, business.industry, Computer science, 010102 general mathematics, Transmitter, Chaotic, 02 engineering and technology, Electronic circuit design, Encryption, 01 natural sciences, Synchronization, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear Sciences::Chaotic Dynamics, 020901 industrial engineering & automation, Filter (video), Electronic engineering, Demodulation, 0101 mathematics, business, Realization (systems), Computer Science::Information Theory
Abstract

International audience; In this study, a new approach for secure communications over noisy receiver is presented with the electronic circuit design. Two chaotic systems are used in this approach, the first is the time-delay Liu chaotic system which is used to establish the synchronization between the transmitter and the nosing receiver using LMI H $\infty$ control approach also used to encrypt the transmitted message which is injected in the second chaotic system in the transmitter. to recover the message, the demodulation with the subsystem of the Akgul chaotic system is proposed. The experimental results are corroborated by the numerical computations to show the effectiveness of the proposed approach and the active first order all-pass Filter is used to generate the time-delay.

Published
2017
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5. High performance voltage-sensorless model predictive control for grid integration of packed U ceils based PV system

Author

Mohamed Trabelsi, Sertac Bayhan, Haitham Abu-Rub, Malek Ghanes, Informatique, Biologie Intégrative et Systèmes Complexes (IBISC), Université d'Évry-Val-d'Essonne (UEVE)-Centre National de la Recherche Scientifique (CNRS), Texas A&M University at Qatar, Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Commande (Commande), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), and Commande (LS2N - équipe Commande)

Subjects
Engineering, business.industry, 020209 energy, 020208 electrical & electronic engineering, Photovoltaic system, [SPI.NRJ]Engineering Sciences [physics]/Electric power, Topology (electrical circuits), 02 engineering and technology, Grid, 7. Clean energy, law.invention, Power (physics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Capacitor, Model predictive control, Control theory, law, 0202 electrical engineering, electronic engineering, information engineering, Electronic engineering, Inverter, business, ComputingMilieux_MISCELLANEOUS, Voltage
Abstract

The current energy constraints are pushing researchers to design and optimize power electronic devices for integrating and consuming renewable energy more efficiently. In this paper, a voltage sensorless Model Predictive Control (MPC) solution is proposed for the grid integration of a Packed U Cells (PUC) based PV system. The studied topology is a grid-connected 4-cell 15-level PUC inverter. The control scheme is based on an adaptive observer allowing the appropriate estimation of the capacitors' voltages at each sampling time using the measured grid current. The estimated voltages are then fed to a multi-objective MPC algorithm ensuring the simultaneous regulation of the capacitors' voltages and grid current with low THD. Theoretical analysis and simulation results are given to show the high performance of the proposed solution.

Published
2017
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6. Minimal controllability time for the heat equation under unilateral state or control constraints

Author

Emmanuel Trélat, Enrique Zuazua, Jérôme Lohéac, Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Commande (Commande), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Département Automatique, Productique et Informatique (IMT Atlantique - DAPI), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Control And GEometry (CaGE ), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Departamento de Matemáticas [Madrid], Universidad Autonoma de Madrid (UAM), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Commande (LS2N - équipe Commande), IMT Atlantique (IMT Atlantique), and Universidad Autónoma de Madrid (UAM)

Subjects
0209 industrial biotechnology, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Boundary (topology), 02 engineering and technology, State (functional analysis), 01 natural sciences, Domain (mathematical analysis), Controllability, symbols.namesake, 020901 industrial engineering & automation, Modeling and Simulation, Dirichlet boundary condition, Bounded function, symbols, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Heat equation, Boundary value problem, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Mathematics
Abstract

The heat equation with homogeneous Dirichlet boundary conditions is well known to preserve non-negativity. Besides, due to infinite velocity of propagation, the heat equation is null controllable within arbitrary small time, with controls supported in any arbitrarily open subset of the domain (or its boundary) where heat diffuses. The following question then arises naturally: can the heat dynamics be controlled from a positive initial steady state to a positive final one, requiring that the state remains non-negative along the controlled time-dependent trajectory? We show that this state-constrained controllability property can be achieved if the control time is large enough, but that it fails to be true in general if the control time is too short, thus showing the existence of a positive minimal controllability time. In other words, in spite of infinite velocity of propagation, realizing controllability under the unilateral non-negativity state constraint requires a positive minimal time. We establish similar results for unilateral control constraints. We give some explicit bounds on the minimal controllability time, first in 1D by using the sinusoidal spectral expansion of solutions, and then in the multi-dimensional case. We illustrate our results with numerical simulations, and we discuss similar issues for other control problems with various boundary conditions.

Published
2017
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7. Averaged controllability of parameter dependent conservative semigroups

Author

Enrique Zuazua, Jérôme Lohéac, Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Commande (LS2N - équipe Commande), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Robotique Et Vivant (LS2N - équipe ReV), Département Automatique, Productique et Informatique (IMT Atlantique - DAPI), IMT Atlantique (IMT Atlantique), Departamento de Matemáticas [Madrid], Universidad Autónoma de Madrid (UAM), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Commande (Commande), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Robotique Et Vivant (ReV), and Universidad Autonoma de Madrid (UAM)

Subjects
0209 industrial biotechnology, perturbation arguments, Parameter dependent systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Perturbation (astronomy), 02 engineering and technology, 01 natural sciences, Schrödinger equation, averaged control, symbols.namesake, 020901 industrial engineering & automation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, Probability measure, Applied Mathematics, Realisation, Diophantine equation, 010102 general mathematics, Mathematical analysis, Wave equation, Controllability, Control system, symbols, Ingham inequal-ities, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], non-harmonic Fourier series, Analysis
Abstract

International audience; We consider the problem of averaged controllability for parameter depending (either in a discrete or continuous fashion) control systems, the aim being to find a control, independent of the unknown parameters, so that the average of the states is controlled. We do it in the context of conservative models, both in an abstract setting and also analysing the specific example of the wave equation. Our first result is of perturbative nature. Assuming the averaging probability measure to be a small parameter-dependent perturbation (in a sense that we make precise) of an atomic measure given by a Dirac mass corresponding to a specific realisation of the system, we show that the averaged controllability property is achieved whenever the system corresponding to the support of the Dirac is controllable. Similar tools can be employed to obtain averaged versions of the so-called Ingham inequalities. Particular attention is devoted to 1d wave and Schrödinger equations in which the time-periodicity of solutions can be exploited to obtain more precise results, provided the parameters involved satisfy Diophantine conditions ensuring the lack of resonances.

Published
2017
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8. Time optimal control for a perturbed Brockett integrator

Author

Lohéac, Jérôme, Scheid, Jean-Francois, Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Commande (Commande), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), and Commande (LS2N - équipe Commande)

Subjects
State constraints, Computer Science::Systems and Control, Time optimal controllability, Brockett integrator, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Numerical resolution, Micro-swimmers
Abstract

International audience; The aim of this work is to compute time optimal controls for a perturbation of a Brockett integrator with state constraints. Brockett integrator and its perturbations appears in many applications fields. One of them described in details in this note is the swimming of microorganisms. We present some key results for a fast and robust numerical method to compute time optimal controls for the perturbation of a Brockett integrator. This numerical method is based on explicit formulae of time optimal controls for the Brockett integrator. The methodology presented in this work is applied to the time optimal control of a micro-swimmer.

Published
2017
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