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 trajectories, under positivity constraints on the control or the state, of a one-dimensional heat equation involving the fractional Laplace operator (−∂2x)s (with 0<s<1) on 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…

#### Null controllability of a nonlocal heat equation with an additive integral kernel

U. Biccari, V. Hernández-Santamaría Null controllability of a nonlocal heat equation with integral kernel. SIAM J. Control Optim., Vol. 57, No. 4 (2019), pp. 2924-2938, DOI: 10.1137/18M1218431 Abstract: We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel.…

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

U. Biccari, M. Warna Null-controllability properties of a fractional wave equation with a memory term Abstract: We study the null-controllability properties of a one-dimensional wave equation with memory associated with the fractional Laplace operator. The goal is not only to drive the displacement and the velocity to rest at some time-instant but also to require…

#### 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 Abstract: In this paper, we analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian $(-\Delta)^s$ ($0

#### Null-controllability properties of the wave equation with a second order memory term

U. Biccari, S. Micu Null-controllability properties of the wave equation with a second order memory termJ DIFFER EQUATIONS, Vol. 267, No. 2 (2019), pp. 1376-1422 doi.org/10.1016/j.jde.2019.02.009 Abstract: We study the internal controllability of a wave equation with memory in the principal part, defined on the one-dimensional torus $\mathbb{T}=\mathbb{R}/2\pi\mathbb{Z}$. We assume that the control is acting…

#### Dynamics and control for multi-agent networked systems: a finite difference approach

U. Biccari, D. Ko, E. Zuazua Dynamics and control for multi-agent networked systems: a finite difference approach. Math. Models Methods Appl. Sci., Vol. 29, No. 4 (2019), pp. 755–790. DOI: 10.1142/S0218202519400050 Abstract: We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic…

#### 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 Abstract: We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both at the continuous and…

#### Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential

U. Biccari Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential, Mathematical Control and related fields, DOI: 10.3934/mcrf.2019011 Abstract: We analyse controllability properties for the one-dimensional heat equation with singular inverse-square potential $u_t-u_{xx}-\frac{\mu}{x^2}u=0\,\,\,(x,t)\in(0,1)\times(0,T)$. For any $\mu

#### 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…