DyCon

Nonuniqueness of minimizers for semilinear optimal control problems

D. Pighin. Nonuniqueness of minimizers for semilinear optimal control problems (2022) J. Eur. Math. Soc, , published online first. https://doi.org/10.4171/jems/1232 Abstract. A counterexample to uniqueness of global minimizers of semilinear…

The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems

C. Esteve, H. Kouhkouh, D. Pighin, E. Zuazua. The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems Abstract: In this work, we analyze the…

Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

Esteve C., Zuazua E.. Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws (2022) Abstract. We give a full characterization of the range of the operator which…

Turnpike in Lipschitz-nonlinear optimal control

Esteve C., Geshkovski G., Pighin D., Zuazua E. . Turnpike in Lipschitz-nonlinear optimal control Nonlinearity. Vol 5. No. 34, pp. 1652-1701 (2022) https://doi.org/10.1088/1361-6544/ac4e61 Abstract. We present a new proof of…

The 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 Numer. Math. 150, 479–519 (2022). https://doi.org/10.1007/s00211-021-01257-w Abstract. We consider the Vlasov-Fokker-Planck equation with random electric…

Constrained control of gene-flow models

bistable equations, Control, geneflow models, non-controllability, reaction-diffusion equations, spatial heterogeneity, staircase method

Mazari I., Ruiz-Balet D., Zuazua E.. Constrained control of gene-flow models. (2021) Ann. Inst. Henri Poincare (C) Anal. Non Lineaire ⟨hal-02373668⟩ Abstract. In ecology and population dynamics, gene-flow refers to…

Differentiability with respect to the initial condition for Hamilton-Jacobi equations

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 equation with a smooth convex…

Control 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 constraints of reaction-diffusion equations arising…

Model predictive control with random batch methods for a guiding problem

Agent-based models, Guiding problem, large scale complex systems, Random

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, pp. 1569-1592. (2021) DOI: https://doi.org/10.1142/S0218202521500329…

Classical system theory revisited for Turnpike in standard state space systems and impulse controllable descriptor systems

descriptor systems, linear systems, long time behavior, optimal control, Riccati equations

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., Vol. 59.5 (2021), pp. 3600-3624 Abstract.…

Optimal 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 in a long time horizon…

Local 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 the Boussinesq system with homogeneous…

Control of Hyperbolic and Parabolic Equations on Networks and Singular limits

advection-diffusion equations, Controllability, cost of controllability, network, singular limits, vanishing viscosity

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 the controllability properties of the…

Controllability 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 this work, we address the…

The turnpike property in semilinear control

D. Pighin The turnpike property in semilinear control ESAIM Control Optim. Calc. Var., Vol. 26 (2021), pp. 1-48 Abstract.An exponential turnpike property for a semilinear control problem is proved. The…

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 Control": Selective harmonic Modulation (SHM)…

Neural ODE Control for Classification, Approximation and Transport

data classification, deep learning, Neural ODEs, Optimal Transport, simultaneous control, transport equations, universal approximation, Wasserstein distance

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 perspective to address some of…

The 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: Design Methods and Applications". Grigory…

Large-time asymptotics in deep learning

deep learning, Neural ODEs, optimal control, Residual Neural Networks, Supervised Learning, turnpike property

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 may roughly be cast as…

Local 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. Math. (2021) https://doi.org/10.1142/S0219199721500036 Abstract. In…

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 Locations": Generally, a prediction problem…

Control 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 during the workshop ”Challenges in…

Internal 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 Schr\"odinger equation involving the fractional…

Nonnegative control of finite-dimensional linear systems

Dirac impulse, Minimal time, Nonnegative control

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 Abstract. We consider the controllability…

Rotor 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 is given. We determine the…

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 control for heat equations with…

The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

Hamilton-Jacobi equation, inverse design problem, obstacle problems, 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 Abstract. We study the inverse…

Null-controllability of perturbed porous medium gas flow

degenerate parabolic equation, null controllability, porous medium equation, thin-ﬁlm equation

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 a nonlinear degenerate parabolic equation,…

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 Supervised Learning and Unsupervised Learning,…

Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations

Constraints, Controllability, Mathematical biology, Reaction-diffusion

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. Dynamic phenomena in social and…

Sparse source identification of linear diffusion–advection equations by adjoint methods

Adjoint problem, Diffusion–advection equation, Inverse problems, optimal control, Optimization

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 an algorithm for the time-inversion…

The 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 state equation and/or detectability in…

Controllability of a Class of Infinite Dimensional Systems with Age Structure

admisible control operator, age structure, infinite dimensional linear system, null controllability, population dynamics

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. 231-260 hal-01964612v2 Abstract: Given a…

Shape turnpike for linear parabolic PDE models

Direct methods, Optimal shape design, Parabolic equation, Strict dissipativity, Turnpike

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 study the turnpike property for…

A stochastic approach to the synchronization of coupled oscillators

coupled oscillators, gradient descent, Kuramoto model, optimal control, random batch method, synchronization

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). DOI: 10.3389/fenrg.2020.00115 Abstract. This paper…

Full probabilistic solution of a infinite dimensional linear control system with random initial and final conditions

finite dimensional, linear control system, probabilistic

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 conditions. J. Franklin I. (2020)…

Turnpike in optimal shape design

Direct methods, heat equation, Optimal shape design, Strict dissipativity, Turnpike

G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design IFAC-PapersOnline, Vol. 52, No. 16 (2019), pp. 496-501, ISSN: 24058963, DOI: 10.1137/17M1119160 Abstract: We investigate the turnpike problem in…

Stochastic 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 for the simultaneous control of…

Asymptotic behavior and control of a “guidance by repulsion” model

Asymptotic stability, Collective behavior, Guidance by repulsion, Herding, optimal control

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 (2020).DOI:10.1142/S0218202520400047 Abstract. We model and…

Stochastic persistency of nematic alignment state for the Justh-Krishnaprasad model with additive white noises

Alignment, emergence, Justh–Krishnaprasad model, nematic alignment, stochastic 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 Methods Appl. Sci. Vol. 30,…

The turnpike property in nonlinear optimal control – A geometric approach

dynamical system theory, general dynamical systems, geometric approach, nonlinear optimal control, optimal control problems, turnpike property, turnpike-like property

N. Sakamoto, D. Pighin, E. Zuazua The turnpike property in nonlinear optimal control - A geometric approach. IEEE 58th Conference on Decision and Control (CDC) (2020). DOI: 10.1109/CDC40024.2019.9028863 Abstract: This paper…

Controllability 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

A 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 the recent works [9, 17,…

DyCon blog: Inverse problem for Hamilton-Jacobi equations

Spain. 03.04.2020. Today, our team member Carlos Esteve made a contribution to the DyCon Blog about "Inverse problem for Hamilton-Jacobi equations": Inverse design problem for Hamilton-Jacobi equations: projection on the…

Asymptotic 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 scalar convection-diffusion equations set in…

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 Burgers Equation": "The DMD approach…

A 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 to describe mixed traffic with…

Emergent collective behaviors of stochastic kuramoto oscillators

Kuramoto model, mean-field limit, multiplicative noise, random environment, synchronization

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. We study the collective dynamics…

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 a cart with DyCon Toolbox".…

Null-controllability properties of a fractional wave equation with a memory term

fractional wave equation, memory term, null controllability

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. 399-430 Abstract: We study the…

Existence 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 following degenerate/singular parabolic equation ,…

Propagation 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., Vol. 20 (2020), pp. 1401-1438. DOI: 10.1007/s10208-020-09445-0 Abstract: We analyze…

Output controllability in a long-time horizon

Averaged control, Controlled invariant subspace, Linear optimal control, Open-loop control systems, Output controllability

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 dimensional system. Our aim is…

A 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 flow on road networks. Most…

On 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 problem, which can be modeled…

Optimal 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 using a small number of…

Inverse 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 one-dimensional Burgers equation. This problem…

Single-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, DOI: 10.1016/j.matpur.2019.12.006 Abstract. We consider…

Controllability 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. We study the controllability to…

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 this tutorial, we present some…

Model 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 advanced tools and methods for…

DyCon 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 our last dissemination posts about…

Turnpike 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 control, we focus on the…

Numerical aspects of LTHC of Burgers equation

c++

Download Code related to the Numerical aspects of LTHC of Burgers equation. Developed by Navid Allahverdi, , Alejandro Pozo & Enrique Zuazua

Python

PYTHON: https://www.python.org/

C++

C++: http://www.cplusplus.com/

Optimal Control of the Poisson Equation with OpenFOAM

OPENFOAM

Download Code related to the Optimal Control of the Poisson Equation with OpenFOAM. Developed by Víctor Hernández-Santamaría, José Vicente Lorenzo & Enrique Zuazua

Openfoam

OPENFOAM: https://www.openfoam.com

WKB expansion for a fractional Schrödinger equation with applications to controllability

MATLAB

Download Code related to the WKB expansion for a fractional Schrödinger equation with applications to controllability. Developed by Umberto Biccari, Alejandro B. Aceves & Enrique Zuazua

Turnpike property for functionals involving L¹−norm

MATLAB

Download Code related to the Turnpike property for functionals involving L¹−norm. Developed by Martin Lazar, Cesare Molinari & Enrique Zuazua

Control of the semi-discrete 1D heat equation under nonnegative control constraint

IpOpt/AMPL

Download Code related to the Control of the semi-discrete 1D heat equation under nonnegative control constraint. Developed by Jérôme Lohéac, Emmanuel Trélat & Enrique Zuazua

Solving an optimal control problem arised in ecology with AMPL

IpOpt/AMPL

Download Code related to the Solving an optimal control problem arised in ecology with AMPL . Developed by Jiamin ZHU & Enrique Zuazua

$plot_frac_schrodinger2_09_6$

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 equation \begin{align}\label{main_eq} \mathcal{P}_s u:= \left[i\partial_t…

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 order to solve control problems…

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 and AMPL in order to…

Averaged 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

MATLAB

Download Code related to the Finite element approximation of the 1-D fractional Poisson equation problem. Developed by Umberto Biccari, Victor Hernández-Santamaría & Enrique Zuazua .

Greedy optimal control for elliptic problems and its application to turnpike problems MATLAB code

MATLAB

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 the notion of averaged control…

Averaged control MATLAB code

MATLAB

Download Code related to the Averaged control problem. Developed by Víctor Hernández-Santamaría, José Vicente Lorenzo & Enrique Zuazua.

Wavecontrol MATLAB code

MATLAB

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

MATLAB

Download Code related to the Greedy algorithm for Parametric Vlasov-Fokker-Planck System. Developed by Yuhua Zhu & Enrique Zuazua.

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 a free software to compute…

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 f =\frac{\sigma_3}{\epsilon}\delta\pt_v\ (v f +\delta\pt_vf\…

Kolmogorov Equation Freefem++ code

freefem++

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 of an introduced population of…

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 and $v$ a potential function.…

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 aerodynamics [1, 4]. During the…

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 with Dirichlet boundary conditions where…

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 the minimal computed time $T\simeq\mathtt{0.2093}$.…

$Finite element approximation of the 1-D fractional Poisson equation$

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.

Turnpike property for functionals involving L<sup>1</sup>−norm

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 minimize a weighted distance to…

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...

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...

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...

IpOpt/AMPL code sample

IpOpt/AMPL

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

MATLAB

Download Code related to the Greedy Control problem. Developed by Martin Lazar & Enrique Zuazua.

Optimal control applied to collective behaviour

The standard approach for solving a driving problem is a leadership strategy, based on the attraction that a driver agent exerts on other agent. Repulsion forces are mostly used for collision avoidance, defending a target or describing the need for personal space. We present a “guidance by repulsion” model describing the behaviour of two agents, a driver and an evader...