A theoretical investigation of Brockett's ensemble optimal control problems

DOI10.1007/s00526-019-1604-2zbMath1423.49021arXiv1809.09904OpenAlexW2972223792WikidataQ127285759 ScholiaQ127285759MaRDI QIDQ2274390

Souvik Roy, Jan Bartsch, Francesco Fanelli, Alfio Borzì

Publication date: 19 September 2019

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.09904

zbMATH Keywords

Liouville equationcost functionalsBrockett's ensemble optimal control problemsunbounded drift function

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Smoothness and regularity of solutions to PDEs (35B65) Existence theories for optimal control problems involving partial differential equations (49J20) PDEs in connection with control and optimization (35Q93) Initial value problems for first-order hyperbolic equations (35L03)

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Cites Work

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• Transport equation and Cauchy problem for BV vector fields
• Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices
• Ordinary differential equations, transport theory and Sobolev spaces
• Para-differential calculus and applications to the Cauchy problem for nonlinear systems
• Functional analysis, Sobolev spaces and partial differential equations
• The Fokker-Planck equation. Methods of solution and applications.
• Quantum Optimal Control Problems with a Sparsity Cost Functional
• Fourier Analysis and Nonlinear Partial Differential Equations
• Convexity and Optimization in Banach Spaces
• Averaged time-optimal control problem in the space of positive Borel measures
• Continuity equations and ODE flows with non-smooth velocity
• Stable signal recovery from incomplete and inaccurate measurements
• Singular limits in thermodynamics of viscous fluids

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