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…

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…