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

Hernández-Santamaría V., Lazar M., Zuazua E. Greedy optimal control for elliptic problems and itsapplication to turnpike problems DOI: 10.1007/s00211-018-1005-z Abstract: We adapt and apply greedy methods to approximate in an efficient way the optimalcontrols for parameterized elliptic control problems. Our results yield an optimal approximation procedure that, in particular, performs better than simply sampling theparameter-space…

Corrigendum and addendum to “Hierarchic control for a coupled parabolic system”

Hernández-Santamaría V., de Teresa L., Poznyak A. Corrigendum and addendum to “Hierarchic control for a coupled parabolic system” , DOI: 10.4171/PM/1998 Abstract: In [2] we used three controls for a system of two coupled parabolic equations. We defined three functionals to be minimized and a hierarchy on the controls obtaining from the optimality condition a…

Insensitizing controls for a semilinear parabolic equation: a numerical approach

Hernández-Santamaría V., de Teresa L., Boyer, F. Insensitizing controls for a semilinear parabolic equation: a numerical approach , DOI: Abstract: In this paper, we study the insensitizing control problem in the discrete setting of finite-differences. We prove the existence of a control that insensitizes the norm of the observed solution of a 1-D semidiscrete parabolic…

Robust Stackelberg controllability for linear and semilinear heat equations

Hernández-Santamaría V., de Teresa L. Robust Stackelberg controllability for linear and semilinear heat equations , DOI: Abstract: In this paper we study a Stackelberg–Nash strategy to control systems of coupled linear parabolic partial differential equations. We assume that we can act on the system through several controls called followers, intended to solve a Nash multi-objective…

Some remarks on the hierarchic control for coupled parabolic PDEs

Hernández-Santamaría V., de Teresa L. Some remarks on the hierarchic control for coupled parabolic PDEs , DOI: To appear Abstract: In this paper, we study Stackelberg-Nash strategies to control a system of two coupled parabolic equations. We assume that we act in the system by means of a hierarchy of controls. First, controls in each…

The Poisson equation from non-local to local

U. Biccari, V. Hernández-Santamaría The Poisson equation from non-local to local, Electronic Journal of Differential Equations, Vol. 2018 (2018), No. 145, pp. 1-13. DOI: arXiv:1801.09470 Abstract: We analyze the limit behavior as $s\to 1^-$ of the solution to the fractional Poisson equation $\fl{s}{u_s}=f_s$, $x\in\Omega$ with homogeneous Dirichlet boundary conditions $u_s\equiv 0$, $x\in\Omega^c$. We show that…

Hierarchic control for a coupled parabolic system

Hernández-Santamaría V., de Teresa L., Poznyak A. Hierarchic control for a coupled parabolic system , DOI: 10.4171/PM/1979 Abstract: In this paper we study a Stackelberg–Nash strategy to control systems of coupled linear parabolic partial differential equations. We assume that we can act on the system through several controls called followers, intended to solve a Nash…

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

Hernández-Santamaría V., Lazar M., Zuazua E. , DOI: 10.1007/s00211-018-1005-z Abstract: In this paper, we deal with the approximation of optimal controls for parameter-dependent elliptic and 7 parabolic equations. We adapt well-known results on greedy algorithms to approximate in an efficient 8 way the optimal controls for parameterized elliptic control problems. Our results yield an optimal…

Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects

U. Biccari, V. Hernández-Santamaría Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects, IMA Journal of Mathematical Control and Information DOI: 10.1093/imamci/dny025 Abstract: We analyze the controllability problem for a one-dimensional heat equation involving the fractional Laplacian $(-d^2_x)^s$ on the interval $(-1,1)$. Using classical results and techniques, we show that, acting from an…