Optimal Neumann Boundary Control of a Vibrating String with Uncertain Initial Data and Probabilistic Terminal Constraints

DOI10.1137/19M1269944zbMath1446.49004OpenAlexW3047563290WikidataQ104129224 ScholiaQ104129224MaRDI QIDQ5117357

Martin Gugat, Mohammad Hassan Farshbaf-Shaker, Holger Heitsch, René Henrion

Publication date: 21 August 2020

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1269944

zbMATH Keywords

optimal controlboundary controlwave equationprobabilistic constraintterminal constraintuncertain initial data

Mathematics Subject Classification ID

Numerical methods based on nonlinear programming (49M37) Existence theories for optimal control problems involving partial differential equations (49J20) Existence of optimal solutions to problems involving randomness (49J55) Problems with incomplete information (optimization) (49N30)

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Cites Work

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• A smoothing function approach to joint chance-constrained programs
• Isentropic fluid dynamics in a curved pipe
• Coupling conditions for gas networks governed by the isothermal Euler equations
• Random data Cauchy theory for supercritical wave equations I: Local theory
• Computation of multivariate normal and \(t\) probabilities
• Regularization of \(L^\infty\)-optimal control problems for distributed parameter systems
• Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization
• Subdifferential characterization of probability functions under Gaussian distribution
• A joint model of probabilistic/robust constraints for gas transport management in stationary networks
• Norm-minimal Neumann boundary control of the wave equation
• Flows on networks: recent results and perspectives
• Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization
• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• On Random Fourier Series
• Sensitivity Analysis of Optimal Control Problems for Wave Equations
• Solving chance constrained optimal control problems in aerospace via kernel density estimation
• Stochastic Dominance Constraints in Elastic Shape Optimization
• Optimal Control of PDEs under Uncertainty
• Conditional-Value-at-Risk Estimation via Reduced-Order Models
• Gradient Formulae for Nonlinear Probabilistic Constraints with Gaussian and Gaussian-Like Distributions
• Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
• L^p-Optimal Boundary Control for the Wave Equation
• Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods
• An Inner-Outer Approximation Approach to Chance Constrained Optimization
• Subroutines for computing normal probabilities of sets -- computer experiences