Esteve C., Zuazua E.. Differentiability with respect to the initial condition for Hamilton-Jacobi equations (2021) Abstract. We prove that the viscosity solution to a Hamilton-Jacobi…
View More Differentiability with respect to the initial condition for Hamilton-Jacobi equationsCategory: DyCon
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View More Protected: DyCon BlogControl of certain parabolic models from biology and social sciences
Domènec Ruiz-Balet, , Enrique Zuazua. Control of certain parabolic models from biology and social sciences (2021) Abstract. These lecture notes address the controllability under state…
View More Control of certain parabolic models from biology and social sciencesThe Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term
Shi Jin, Yuhua Zhu, Enrique Zuazua. The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term (2021) Numer Math (Heidelb) Abstract. We consider the Vlasov-Fokker-Planck equation…
View More The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing TermModel predictive control with random batch methods for a guiding problem
Ko Dongnam, Zuazua Enrique. Model predictive control with random batch methods for a guiding problem (2021). Math. Models Methods Appl. Sci., Vol. 31, No. 8,…
View More Model predictive control with random batch methods for a guiding problemClassical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems
Heiland J., Zuazua E. Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems (2021) SIAM J. Control Optim. Abstract.…
View More Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systemsOptimal control for neural ODE in a long time horizon and applications to the classification and simultaneous controllability problems
Jon Asier Bárcena-Petisco. Optimal control for neural ODE in a long time horizon and applications to the classification (2021) Abstract. We study the optimal control…
View More Optimal control for neural ODE in a long time horizon and applications to the classification and simultaneous controllability problemsLocal null controllability of the penalized Boussinesq system with a reduced number of controls
J.A. Bárcena-Petisco, Kevin Le Balc’H. Local null controllability of the penalized Boussinesq system with a reduced number of controls (2021) Abstract. In this paper we consider…
View More Local null controllability of the penalized Boussinesq system with a reduced number of controlsControl of Hyperbolic and Parabolic Equations on Networks and Singular limits
J.A. Bárcena-Petisco, M. Cavalcante, G.M. Coclite, N. de Nitti, Enrique Zuazua. Control of Hyperbolic and Parabolic Equations on Networks and Singular limits (2021) Abstract. We study…
View More Control of Hyperbolic and Parabolic Equations on Networks and Singular limitsControllability of one-dimensional viscous free boundary flows
B. Geshkovski, E. Zuazua. Controllability of one-dimensional viscous free boundary flows. Siam. J. Control. Optim (2021), Vol. 59, No. 3, pp. 1830–1850. https://doi.org/10.1137/19M1285354 Abstract. In…
View More Controllability of one-dimensional viscous free boundary flowsThe turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation
C. Esteve, H. Kouhkouh, D. Pighin, E. Zuazua. The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation Abstract: In this work, we analyze the…
View More The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equationThe turnpike property in semilinear control
D. Pighin The turnpike property in semilinear control ESAIM Control Optim. Calc. Var (2021) Abstract.An exponential turnpike property for a semilinear control problem is proved.…
View More The turnpike property in semilinear controlNonuniqueness of minimizers for semilinear optimal control problems
D. Pighin. Nonuniqueness of minimizers for semilinear optimal control problems. J Eur. Math. Soc. (2021) Abstract. A counterexample to uniqueness of global minimizers of semilinear…
View More Nonuniqueness of minimizers for semilinear optimal control problemsConstrained control of gene-flow models
Mazari I., Ruiz-Balet D., Zuazua E.. Constrained control of gene-flow models. (2021) ⟨hal-02373668⟩ Abstract. In ecology and population dynamics, gene-flow refers to the transfer of…
View More Constrained control of gene-flow models
DyCon blog: Multilevel Selective Harmonic Modulation via Optimal Control
Spain. 12.04.2021. Our team members Deyviss Jesús Oroya-Villalta, Carlos Esteve-Yagüe and Umberto Biccari, made a contribution to the DyCon Blog about “Multilevel Selective Harmonic Modulation via Optimal…
View More DyCon blog: Multilevel Selective Harmonic Modulation via Optimal ControlNeural ODE Control for Classification, Approximation and Transport
Ruiz-Balet D., Zuazua E. Neural ODE Control for Classification, Approximation and Transport (2021) Abstract. We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical…
View More Neural ODE Control for Classification, Approximation and TransportThe Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking Terms
M. Gugat, M. Schuster, E. Zuazua. The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-Smooth Tracking Terms, in “Stabilization of Distributed Parameter Systems:…
View More The Finite-Time Turnpike Phenomenon for Optimal Control Problems: Stabilization by Non-smooth Tracking TermsLarge-time asymptotics in deep learning
Esteve C., Geshkovski B., Pighin D., Zuazua E. Large-time asymptotics in deep learning (2021). hal-02912516 Abstract. It is by now well-known that practical deep supervised learning…
View More Large-time asymptotics in deep learningLocal null controllability of a model system for strong interaction between internal solitary waves
Jon Asier Bárcena-Petisco, Sergio Guerrero and Ademir F. Pazoto. Local null controllability of a model system for strong interaction between internal solitary waves. Commun. Contemp.…
View More Local null controllability of a model system for strong interaction between internal solitary waves
DyCon blog: Points of Interest Extraction and Prediction of Next Locations
Spain. 10.03.2021. Aicha Karite recent member from our team, made a contribution to the DyCon Blog about “Points of Interest Extraction and Prediction of Next…
View More DyCon blog: Points of Interest Extraction and Prediction of Next LocationsControl and Deep Learning: Some connections
B. Geshkovski, E. Zuazua. Control and Deep Learning: Some connections (2021) This note is an extended abstract for a talk given by the second author…
View More Control and Deep Learning: Some connectionsInternal control for a non-local Schrödinger equation involving the fractional Laplace operator
U. Biccari Internal control for a non-local Schrödinger equation involving the fractional Laplace operator (2021) Abstract: We analyze the interior controllability problem for a nonlocal…
View More Internal control for a non-local Schrödinger equation involving the fractional Laplace operatorNonnegative control of finite-dimensional linear systems
Lohéac J., Trélat E., Zuazua E. Nonnegative control of finite-dimensional linear systems. Ann. I. H. Poincare-An., Vol. 38, No. 2, pp. 301-346. (2021) DOI: https://doi.org/10.1016/j.anihpc.2020.07.004…
View More Nonnegative control of finite-dimensional linear systemsRotor imbalance suppression by optimal control
M. Gnuffi, D. Pighin, N. Sakamoto Rotor imbalance suppression by optimal control (2021) Abstract. An imbalanced rotor is considered. A system of moving balancing masses…
View More Rotor imbalance suppression by optimal control
DyCon blog: Averaged dynamics and control for heat equations with random diffusion
Spain. 04.12.2020. Our team member Jon Asier Bárcena Petisco and our Head Enrique Zuazua made a contribution to the DyCon Blog about “Averaged dynamics and…
View More DyCon blog: Averaged dynamics and control for heat equations with random diffusionTurnpike in Lipschitz-nonlinear optimal control
Esteve C., Geshkovski G., Pighin D., Zuazua E. . Turnpike in Lipschitz-nonlinear optimal control (2020) Abstract. We present a new proof of the turnpike property…
View More Turnpike in Lipschitz-nonlinear optimal controlThe Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes
Esteve C., Zuazua E.. The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes SIAM J. Math. Anal., Vol. 52, No. 6, pp. 5627–5657 (2020). https://doi.org/10.1137/20M1330130…
View More The Inverse Problem for Hamilton-Jacobi equations and Semiconcave EnvelopesNull-controllability of perturbed porous medium gas flow
B. Geshkovski,Null-controllability of perturbed porous medium gas flow. ESAIM:COCV, vol. 26, No. 85 (2020). DOI: 10.1051/cocv/2020009 Abstract: In this work, we investigate the null-controllability of…
View More Null-controllability of perturbed porous medium gas flow
DyCon blog: Q-learning for finite-dimensional problems
Spain. 29.10.2020. Our team member Carlos Esteve made a contribution to the DyCon Blog about “Q-learning for finite-dimensional problems“: Reinforcement Learning (RL) is, together with…
View More DyCon blog: Q-learning for finite-dimensional problemsControl under constraints for multi-dimensional reaction-diffusion monostable and bistable equations
Ruiz-Balet D., Zuazua E.. Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations. J. Math. Pures Appl, vol. 143, pp. 345-375 (2020) https://doi.org/10.1016/j.matpur.2020.08.006 Abstract.…
View More Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equationsSparse source identification of linear diffusion–advection equations by adjoint methods
Monge A., Zuazua E. Sparse source identification of linear diffusion–advection equations by adjoint methods. Syst. Control. Lett, vol. 145 (2020). DOI: https://doi.org/10.1016/j.sysconle.2020.104801 Abstract: We present…
View More Sparse source identification of linear diffusion–advection equations by adjoint methodsThe turnpike with lack of observability
Pighin D., Sakamoto N. The turnpike with lack of observability (2020) Abstract: We obtain turnpike results for optimal control problems with lack of stabilizability in the…
View More The turnpike with lack of observabilityControllability of a Class of Infinite Dimensional Systems with Age Structure
Maity D., Tucsnak M., Zuazua E. Controllability of a Class of Infinite Dimensional Systems with Age Structure. Control Cybern. Vol. 48 (2020), No. 2, pp.…
View More Controllability of a Class of Infinite Dimensional Systems with Age StructureShape turnpike for linear parabolic PDE models
Lance G., Trélat E., Zuazua E. Shape turnpike for linear parabolic PDE models Syst. Control. Lett. Vol. 142 (2020). DOI: 10.1016/j.sysconle.2020.104733 Abstract: We introduce and…
View More Shape turnpike for linear parabolic PDE modelsA stochastic approach to the synchronization of coupled oscillators
Umberto Biccari, Enrique Zuazua. A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, section Smart Grids. Front. Energy Res. Vol. 8 (2020).…
View More A stochastic approach to the synchronization of coupled oscillatorsFull probabilistic solution of a infinite dimensional linear control system with random initial and final conditions
J.-C. Cortes, A. Navarro-Quiles, J.-V. Romero, M.-D. Rosello, E. Zuazua. Full probabilistic solution of a infinite dimensional linear control system with random initial and final…
View More Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditionsTurnpike in optimal shape design
G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design IFAC-PAPERSONLINE. (ISSN: 24058963). 52(16): 496-501. DOI: 10.1137/17M1119160 Abstract: We investigate the turnpike problem in…
View More Turnpike in optimal shape designStochastic optimization methods for the simultaneous control of parameter-dependent systems
Umberto Biccari, Ana Navarro-Quiles, Enrique Zuazua. Stochastic optimization methods for the simultaneous control of parameter-dependent systems (2020) Abstract. We address the application of stochastic optimization methods…
View More Stochastic optimization methods for the simultaneous control of parameter-dependent systemsAsymptotic behavior and control of a “guidance by repulsion” model
Dongnam Ko, E. Zuazua, Asymptotic behavior and control of a “guidance by repulsion” model. Math Models Methods Appl. Sci. Vol. 30, No. 04, pp. 765-804…
View More Asymptotic behavior and control of a “guidance by repulsion” modelStochastic persistency of nematic alignment state for the Justh-Krishnaprasad model with additive white noises
Seung-Yeal Ha, Dongnam Ko, Woojoo Shim, Hui Yu, . Stochastic persistency of nematic alignment state for the Justh-Krishnaprasad model with additive white noises. Math Models…
View More Stochastic persistency of nematic alignment state for the Justh-Krishnaprasad model with additive white noisesThe turnpike property in nonlinear optimal control – A geometric approach
N. Sakamoto, D. Pighin, E. Zuazua The turnpike property in nonlinear optimal control – A geometric approach. IEEE 58th Conference on Decision and Control (CDC)…
View More The turnpike property in nonlinear optimal control – A geometric approach
DyCon blog: Inverse problem for Hamilton-Jacobi equations
Spain. 22.04.2020. Today, our team member Carlos Esteve made a contribution to the DyCon Blog about “Inverse problem for Hamilton-Jacobi equations“: Inverse design problem for…
View More DyCon blog: Inverse problem for Hamilton-Jacobi equationsA fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models
I. Mazari, D. Ruiz-Balet. A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models (2020) Abstract. Following…
View More A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive modelsAsymptotic behavior of scalar convection-diffusion equations
Enrique Zuazua. Asymptotic behavior of scalar convection-diffusion equations (2020) Abstract. In these lecture notes, we address the problem of large-time asymptotic behaviour of the solutions to…
View More Asymptotic behavior of scalar convection-diffusion equations
DyCon Blog: POD and DMD Reduced Order Models for a 2D Burgers Equation
Spain. 11.03.2020. Today, our team member Jan Heiland made a contribution to the DyCon Blog about “POD and DMD Reduced Order Models for a 2D…
View More DyCon Blog: POD and DMD Reduced Order Models for a 2D Burgers EquationA PDE-ODE model for traffic control with autonomous vehicles
Thibault Liard, Raphael Stern, Maria Laura Delle Monache. A PDE-ODE model for traffic control with autonomous vehicles. (2020) Abstract. We introduce a coupled PDE-ODEs model…
View More A PDE-ODE model for traffic control with autonomous vehiclesEmergent collective behaviors of stochastic kuramoto oscillators
Seung-Yeal Ha, Dongnam Ko, Chanho Min, Xiongtao Zhang. Emergent collective behaviors of stochastic kuramoto oscillators. Vol. 25, No. 3, pp. 1059-1081 (2020) DOI: 10.3934/dcdsb.2019208 Abstract.…
View More Emergent collective behaviors of stochastic kuramoto oscillators
DyCon Blog: Stabilization of a double pendulum on a cart with DyCon Toolbox
Spain. 14.02.2020. Yesterday, our team members Jesús Oroya and Jorge Mallo made a contribution to the DyCon Blog about “Stabilization of a double pendulum on…
View More DyCon Blog: Stabilization of a double pendulum on a cart with DyCon ToolboxNull-controllability properties of a fractional wave equation with a memory term
U. Biccari, M. Warma Null-controllability properties of a fractional wave equation with a memory term. Evol. Eq. Control The., Vol. 9, No. 2 (2020), pp.…
View More Null-controllability properties of a fractional wave equation with a memory termExistence and cost of boundary controls for a degenerate/singular parabolic equation
Umberto Biccari, Víctor Hernández-Santamaría, Judith Vancostenoble. Existence and cost of boundary controls for a degenerate/singular parabolic equation (2020). Abstract. In this paper, we consider the…
View More Existence and cost of boundary controls for a degenerate/singular parabolic equationPropagation of one and two-dimensional discrete waves under finite difference approximation
U. Biccari, A. Marica, E. Zuazua Propagation of one and two/dimensional discrete waves under finite difference approximation,Found Comput Math (2020). DOI: 10.1007/s10208-020-09445-0 Abstract: We analyze…
View More Propagation of one and two-dimensional discrete waves under finite difference approximationOutput controllability in a long-time horizon
Martin Lazar, Jerôme Lohéac. Output controllability in a long-time horizon. Automatica, Vol. 113 (2020). DOI: 10.1016/j.automatica.2019.108762 Abstract. In this article we consider a linear finite…
View More Output controllability in a long-time horizonA controlled multiscale model for traffic regulation via autonomous vehicles
T. Liard, . A controlled multiscale model for traffic regulation via autonomous vehicles. (2019) Abstract. Autonomous vehicles ($AV$s) allow new ways of regulating the traffic…
View More A controlled multiscale model for traffic regulation via autonomous vehiclesOn entropic solutions to conservation laws coupled with moving bottlenecks
T. Liard, Benedetto Piccoli. On entropic solutions to conservation laws coupled with moving bottlenecks. (2019) Abstract. Moving bottlenecks in road traffic represent an interesting mathematical…
View More On entropic solutions to conservation laws coupled with moving bottlenecksOptimal driving strategies for traffic control with autonomous vehicles
T. Liard, Raphael Stern, Maria Laura Delle Monache. Optimal driving strategies for traffic control with autonomous vehicles. (2019) Abstract. This article considers the possibility of…
View More Optimal driving strategies for traffic control with autonomous vehiclesInverse design for the one-dimensional Burgers equation
T. Liard, E. Zuazua. Inverse design for the one-dimensional Burgers equation. (2019) Abstract. In this paper, we study the problem of inverse design for the…
View More Inverse design for the one-dimensional Burgers equationSingle-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature
C. Esteve Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvatureJ MATH PURE APPL, Vol 137 (2020) pp. 143-177,…
View More Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvatureControllability properties from the exterior under positivity constraints for a 1-D fractional heat equation
Antil H, Biccari U, Ponce R, Warma M, Zamorano S. Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation Abstract.…
View More Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation
DyCon blog: Analysis, numerics and control for the obstacle problem
Spain. 15.09.2019. Today, our team member Borjan Geshkovski made a contribution to the DyCon Blog about “Analysis, numerics and control for the obstacle problem“: In…
View More DyCon blog: Analysis, numerics and control for the obstacle problemModel reduction of converter-dominated power systems by Singular Perturbation Theory
U. Biccari, N. Sakamoto, E. Unamuno, D. Madariaga, E. Zuazua, J.A. Barrena. Model reduction of converter-dominated power systems by Singular Perturbation Theory Abstract: The increasing integration of power electronic devices is driving the development of more…
View More Model reduction of converter-dominated power systems by Singular Perturbation TheoryControllability of the one-dimensional fractional heat equation under positivity constraints
U. Biccari, M. Warna, E. Zuazua Internal observability for coupled systems of linear partial differential equations. Commun. Pure Appl. Anal., Vol 19. No. 4 (2019), pp. 1949-1978. DOI: 10.3934/cppaa.2020086
View More Controllability of the one-dimensional fractional heat equation under positivity constraintsDyCon blog
If you are looking for our DyCon ERC project output, don’t miss out: Our DyCon Toolbox for computational methods and tools Our DyCon blog for…
View More DyCon blogA multirate Neumann-Neumann waveform relaxation method for heterogeneous coupled heat equations
A. Monge, P. Birken A multirate Neumann-Neumann waveform relaxation method for heterogeneous coupled heat equations DOI: arXiv:1805.04336 Abstract: An important challenge when coupling two different…
View More A multirate Neumann-Neumann waveform relaxation method for heterogeneous coupled heat equationsTurnpike in optimal shape design for heat equation
G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design for heat equation Abstract: After a short presentation of the turnpike’s problem in optimal…
View More Turnpike in optimal shape design for heat equationNumerical aspects of LTHC of Burgers equation
Python
C++
Optimal Control of the Poisson Equation with OpenFOAM
Openfoam
- OPENFOAM: https://www.openfoam.com
WKB expansion for a fractional Schrödinger equation with applications to controllability
Turnpike property for functionals involving L1−norm
Control of the semi-discrete 1D heat equation under nonnegative control constraint
Solving an optimal control problem arised in ecology with AMPL
WKB expansion for a fractional Schrödinger equation with applications to controllability
PDF version | Download Matlab Code… In [3], we develop a WKB analysis for the propagation of the solutions to the following one-dimensional nonlocal Schrödinger…
View More WKB expansion for a fractional Schrödinger equation with applications to controllability
Optimal Control of the Poisson Equation with OpenFOAM
PDF version | Download Openfoam Code… | In this tutorial, we show how to use the C++ library OpenFOAM (Open Field Operation and Manipulation) in…
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Control of the semi-discrete 1D heat equation under nonnegative control constraint
PDF version… | Download Code… 1 Introduction In the post IpOpt and AMPL use to solve time optimal control problems, we explain how to use IpOpt…
View More Control of the semi-discrete 1D heat equation under nonnegative control constraintAveraged Control SCILAB code
Download Code related to the Averaged control problem.
Developed by Víctor Hernández-Santamaría, José Vicente Lorenzo & Enrique Zuazua.
Finite element approximation of the 1-D fractional Poisson equation MATLAB code
Greedy optimal control for elliptic problems and its application to turnpike problems MATLAB code
Download Code related to the Greedy optimal control for elliptic problems and its application to turnpike problems problem.
Developed by Victor Hernández-Santamaría, Martin Lazar & Enrique Zuazua.
Averaged Control
PDF version | Download Matlab Code | Download Scilab Code | GITHUB In this work, we address the optimal control of parameter-dependent systems. We introduce…
View More Averaged ControlAveraged control MATLAB code
Download Code related to the Averaged control problem.
Developed by Víctor Hernández-Santamaría, José Vicente Lorenzo & Enrique Zuazua.
Wavecontrol MATLAB code
Download Code related to Wavecontrol.
Developed by C. Castro, M. Cea, S. Micu, A. Munch, M. Negreanu & Enrique Zuazua.
MATLAB
- MATHWORKS: https://mathworks.com
Greedy algorithm for Parametric Vlasov-Fokker-Planck System MATLAB code
Wavecontrol
Manual PDF | Download Code… A Matlab guide for the numerical approximation of the exact control and stabilization of the wave equation This webpage contains…
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Greedy algorithm for Parametric Vlasov-Fokker-Planck System
PDF version… | Download Code… 1. Numerical experiments Consider the one dimensional linear Vlasov-Fokker-Planck (VPFP) as following. \begin{equation} \begin{cases} \delta\pt_tf + \sigma_1v\delta\pt_x f – \frac{\sigma_2}{\epsilon} \delta\pt_x\phi\delta\pt_v…
View More Greedy algorithm for Parametric Vlasov-Fokker-Planck SystemKolmogorov Equation Freefem++ code
Download Code related to the Kolmogorov Equation problem.
Developed by Mehmet Ersoy & Enrique Zuazua.
Solving an optimal control problem arised in ecology with AMPL
PDF version… | Download Code… Introduction We are interested in optimal control problems subject to a class of diffusion-reaction systems that describes the growth and spread…
View More Solving an optimal control problem arised in ecology with AMPL
Kolmogorov equation
Read PDF version | Download Code 1 Introduction We are interested in the numerical discretization of the Kolmogorov equation [12] where $\mu>0$ is a diffusive function…
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2D inverse design of linear transport equations on unstructured grids
PDF version… 1. Adjoint estimation: low or high order? Adjoint methods have been systematically associated to the optimal control design [5] and their applications to…
View More 2D inverse design of linear transport equations on unstructured grids
Greedy optimal control for elliptic problems and its application to turnpike problems
PDF version | Download Code… 1. Problem formulation Let $\Omega\subset \mathbb R^d$ be an open and bounded Lipschitz Domain and consider the parameter dependent parabolic equation…
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IpOpt and AMPL use to solve time optimal control problems
PDF version… | Download Code… Featured Video Evolution of the controls and of the state for $y^0=1$, $y^1=5$, $M=20$ and the discretization parameters $N_x=30$, $N_t=450$ in…
View More IpOpt and AMPL use to solve time optimal control problems
Finite element approximation of the 1-D fractional Poisson equation
A finite element approximation of the one-dimensional fractional Poisson equation with applications to numerical control.
View More Finite element approximation of the 1-D fractional Poisson equation
Turnpike property for functionals involving L1−norm
We want to study the following optimal control problem:
\begin{equation*}
\left(\mathcal{P}\right) \ \ \ \ \ \ \ \hat{u}\in\argmin_{u\in L^2_T} \left\{J\left(u\right)=\alpha_c \norm{u}_{1,T} + \frac{\beta}{2}\norm{u}^2_{T}+\alpha_s \norm{Lu}_{1,T} + \frac{\gamma}{2}\norm{Lu-z}_{T}^2\right\},
\end{equation*}
Conservation laws in the presence of shocks
PDF version… The problem We analyze a model tracking problem for a 1D scalar conservation law. It consists in optimizing the initial datum so to…
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Numerical aspects of LTHC of Burgers equation
This issue is motivated by the challenging problem of sonic-boom minimization for supersonic aircrafts, which is governed by a Burgers-like equation. The travel time of the signal to the ground is larger than the time scale of the initial disturbance by orders of magnitude and this motivates our study of large time control of the sonic-boom propagation…
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Long time control and the Turnpike property
The turnpike property establishes that, when a general optimal control problem is settled in large time, for most of the time the optimal control and trajectories remain exponentially close to the optimal control and state of the corresponding steady-state or static optimal control problem…
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Control of PDEs involving non-local terms
Relevant models in Continuum Mechanics, Mathematical Physics and Biology are of non-local nature. Moreover, these models are applied for the description of several complex phenomena for which a local approach is inappropriate or limiting. In this setting, classical PDE theory fails because of non-locality. Yet many of the existing techniques can be tuned and adapted, although this is often a delicate matter…
View More Control of PDEs involving non-local termsIpOpt/AMPL code sample
Download Code related to the IpOpt and AMPL use to solve time optimal control problems.
Developed by Jérôme Lohéac, Emmanuel Trélat & Enrique Zuazua
Greedy Control MATLAB code
Download Code related to the Greedy Control problem.
Developed by Martin Lazar & Enrique Zuazua.