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…

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

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…

Model 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, 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

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.…

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)…

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…

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…

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

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…

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

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

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

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…

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…

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

Shape 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 study the turnpike property for…

A 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). 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

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

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…

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

Stochastic 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 Methods Appl. Sci. Vol. 30,…

The 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) (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

Project name: CONVADP Project reference: CONVADP Funding source: ELKARTEK - Basque Government Duration: March 2020 - December 2021 Principal Investigator (PI): Umberto Biccari About the Project CONVADP is a collaborative…

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…

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…

Emergent 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. 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

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…

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

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…

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…

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…

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…

Road2DC: New Tools for the Design and Control of Hybrid ac/dc Distribution Networks

Project financed by the Basque Government (ELKARTEK programme). Principal Investigator: Jon Andoni Barrena DeustoTech - CCM Coordinator: Enrique Zuazua Iriondo Research Centers: Mondragon University, CCM & Energy (DeustoTech), TECNALIA, Ingeteam & IK4-IKERLAN. Duration: January 2018 - December…

ERC – DyCon: Dynamic Control Project

Funded by ERC - European Research Council Project Acronym: DyConProject Full Title: Dynamic Control and Numerics of Partial Differential Equations Project reference: 694126Principal Investigator: Enrique ZuazuaHost Institutions: DeustoTech - Deusto…

Nonlocal PDEs: Analysis, Control and Beyond

"Nonlocal PDEs: Analysis, Control and Beyond" PI: M. Warma FA9550-18-1-0242, AFOSR - University of Puerto Rico - From June 2018 to May 2021. More information

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…

ConFlex – Control of flexible structures and fluid-structure interactions

ConFlex is funded by the H2020-MSCA-ITN programme (2017-2021) on research & training about the control of flexible structures & fluid-structure interactions. It can be followed on Twitter @ConFlex2017 Conflex project's…

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{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\…

COSNET – Control and Stability of AC/DC hybrid electrical networks

Control y estabilidad de redes híbridas AC/DC: Ecuaciones Diferenciales y Ecuaciones en Derivadas Parciales para el análisis de estabilidad de redes (COSNET) Reference: MTM2017-82996-C2-1-R Fund by: MINECO Research Centers: CCM, DeustoTech & Mondragon…

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…

NUMERIWAVES “New analytical and numerical Methods In Wave propagation”

Project reference: FP7 - 246775 Funded by European Research Council – ERC PI: Enrique Zuazua - BCAM (Bilbao, Basque Country-Spain) Duration: February 2010 - January 2015 Grant Agreement number: FP7…

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…

Diseño óptimo aeronaútico mediante técnicas novedosas

"Diseño óptimo aeronaútico mediante técnicas novedosas". DOMINO, funded by MEC - From 2006 to 2009. (2006-2009) PI: ,

Optimization with PDE Constraints (OPTPDE)

Funded by: European Science Foundation October 2008 - October 2013 More info at http://www.esf.org/optpde

GDRE CONEDP Control of Partial Differential Equations

Duration: January 2010 - December 2014