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 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. While the flow equation is compulsorily solved by means…

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…

Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions

Y. Privat, E. Trélat & E. Zuazua. Spectral shape optimization for the Neumann traces of the Dirichlet-Laplacian eigenfunctions, DOI: 10.1007/s00526-019-1522-3. Abstract: We consider a spectral optimal design problem involving the Neumann traces of the Dirichlet-Laplacian eigenfunctions on a smooth bounded open subset Ω of IRn. The cost functional measures the amount of energy that Dirichlet…

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 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 diffusive equations. We also show that the non-local transport equations commonly derived as the…

Phase portrait control for 1D monostable and bistable reaction-diffusion equations

Pouchol C., Trélat E., Zuazua E. Phase portrait control for 1D monostable and bistable reaction-diffusion equations , DOI: 10.1088/1361-6544/aaf07e Abstract: We consider the problem of controlling parabolic semilinear equations arising in population dynamics, either in finite time or infinite time. These are the monostable and bistable equations on (0,L) for a density of individuals 0≤y(t,x)≤1,…

The turnpike propety in nonlinear optimal control – A geometric approach

N. Sakamoto, D. Pighin, E. Zuazua The turnpike propety in nonlinear optimal control – A geometric approach Abstract: This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic equilibrium and then, apply…