WP4-SINV

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…

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…

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.…

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…

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…

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…

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…

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

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

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

The Inverse Problem for Hamilton-Jacobi equations and Semiconcave Envelopes

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

DyCon blog: Inverse problem for Hamilton-Jacobi equations

A controlled multiscale model for traffic regulation via autonomous vehicles

On entropic solutions to conservation laws coupled with moving bottlenecks

Optimal driving strategies for traffic control with autonomous vehicles

Inverse design for the one-dimensional Burgers equation

Single-point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equation in domains with non-constant curvature

2D inverse design of linear transport equations on unstructured grids

Conservation laws in the presence of shocks

Inverse design and control in the presence of singularities (SINV)

Nonuniqueness of minimizers for semilinear optimal control problems

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

A framework for randomized time-splitting in linear-quadratic optimal control

Numerical Control: Part A

Numerical hypocoercivity for the Kolmogorov equation