I. Mazari, D. Ruiz-Balet, E. Zuazua. Constrained control of bistable reaction-diffusion equations: Gene-flow and spatially heterogeneous models. 2019. ⟨hal-02373668⟩ Abstract. In this article, we study gene-flow models and the influence of spatial heterogeneity on the dynamics of bistable reaction-diffusion equations from the control point of view. We establish controllability results under geometric assumptions on the…
Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations
D. Ruiz-Balet, E. Zuazua. Nonnegative control of finite-dimensional linear systems Abstract. Dynamic phenomena in social and biological sciences can often be modeled employing reaction diffusion equations. Frequently in applications, their control plays an important role when avoiding population extinction or propagation of infectious diseases, enhancing multicultural features, etc. When addressing these issues from a mathematical…
Asymptotic behavior and control of a “guidance by repulsion” model
Dongnam Ko, E. Zuazua. Asymptotic behavior and control of a “guidance by repulsion” model Abstract. We model and analyze a herding problem, where the drivers try to steer the evaders’ trajectories while the evaders always move away from the drivers. This problem is motivated by the guidance-by-repulsion model [Escobedo, R., Ibañez, A. and Zuazua, E.…
Nonnegative control of finite-dimensional linear systems
J. Lohéac, E. Trélat, E. Zuazua. Nonnegative control of finite-dimensional linear systems Abstract. We consider the controllability problem for finite-dimensional linear autonomous control systems with nonnegative controls. Despite the Kalman condition, the unilateral nonnegativity control constraint may cause a positive minimal controllability time. When this happens, we prove that, if the matrix of the system…
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 Abstract. We consider the Vlasov-Fokker-Planck equation with random electric field where the random field is parametrized by countably many infinite random variables due to uncertainty. At the theoretical level, with suitable assumption on the anisotropy of the randomness, adopting the…
Model reduction of converter-dominated power systems by Singular Perturbation Theory
U. Biccari, Noboru Sakamoto, Eneko Unamuno, Danel Madariaga, Enrique Zuazua, Jon Andoni 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 the modeling, analysis, and control of modern power systems to cope with the…
Controllability of one-dimensional viscous free boundary flows
B. Geshkovski, E. Zuazua Controllability of one-dimensional viscous free boundary flows Abstract: In this work, we address the local controllability of a one-dimensional free boundary problem for a fluid governed by the viscous Burgers equation. The free boundary manifests itself as one moving end of the interval, and its evolution is given by the value…
Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids
M. Morales-Hernández, E. Zuazua Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids Comp. Appl. Math. Vol. 38, No. 168 (2019) DOI: 10.1007/s40314-019-0935-0 Abstract: We address the problem of inverse design of linear hyperbolic transport equations in 2D heterogeneous media. We develop numerical algorithms based in gradient-adjoint methodologies on unstructured grids.…
Sparse source identification of linear diffusion–advection equations by adjoint methods
A. Monge, E. Zuazua Sparse source identification of linear diffusion–advection equations by adjoint methods Abstract: We present an algorithm for the time-inversion of diffusion–advection equations, based on the adjoint methodology. Given a final state distribution our main aim is to recover sparse initial conditions, constituted by a finite combination of Dirac deltas, identifying their location…
Turnpike in optimal shape design
G. Lance, E. Trélat, E. Zuazua Turnpike in optimal shape design Abstract: We investigate the turnpike problem in optimal control, in the context of time-evolving shapes. We focus here on the heat equation model where the shape acts as a source term, and we search the optimal time-varying shape, minimizing a quadratic criterion. We first…
