Two Equivalence Theorems of Different Kinds of Optimal Control Problems for Schrödinger Equations

DOI10.1137/130941195zbMath1320.35353arXiv1301.6321OpenAlexW2043766205MaRDI QIDQ5252511

Yubiao Zhang

Publication date: 2 June 2015

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

Full work available at URL: https://arxiv.org/abs/1301.6321

zbMATH Keywords

Schrödinger equationsoptimal controlsoptimal normoptimal timeminimal timeoptimal distanceminimal norm

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Existence theories for optimal control problems involving partial differential equations (49J20) PDEs in connection with control and optimization (35Q93)

Related Items (4)

The bang-bang property of time and norm optimal control problems for parabolic equations with time-varying fractional Laplacian ⋮ Time-optimality by distance-optimality for parabolic control systems ⋮ Quantitative unique continuation for the heat equation with Coulomb potentials ⋮ Observability Inequalities from Measurable Sets for Some Abstract Evolution Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Time optimal controls of the linear Fitzhugh-Nagumo equation with pointwise control constraints
• Bang-bang principle of time optimal controls and null controllability of fractional order parabolic equations
• Bang-bang property for time optimal control of semilinear heat equation
• How violent are fast controls for Schrödinger and plate vibrations?
• Control of the Schrödinger equation
• The Bang-Bang principle of time optimal controls for the heat equation with internal controls
• Internal control of the Schrödinger equation
• On the existence of time optimal controls for linear evolution equations
• Observability and Control of Schrödinger Equations
• Equivalence of Three Different Kinds of Optimal Control Problems for Heat Equations and Its Applications
• The Time Optimal Control with Constraints of the Rectangular Type for Linear Time-Varying ODEs
• Maximum Principle and Bang-Bang Property of Time Optimal Controls for Schrödinger-Type Systems
• An Approach to the Optimal Time for a Time Optimal Control Problem of an Internally Controlled Heat Equation
• Blowup Time Optimal Control for Ordinary Differential Equations
• On the Existence of Time Optimal Controls with Constraints of the Rectangular Type for Heat Equations
• Approximation of Time Optimal Controls for Heat Equations with Perturbations in the System Potential
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Exact Controllability for the Schrödinger Equation
• An Abstract Bang-Bang Principle and Time-Optimal Boundary Control of the Heat Equation
• On the Equivalence of Minimal Time and Minimal Norm Controls for Internally Controlled Heat Equations
• Time optimal control of the heat equation with pointwise control constraints
• $L^\infty$-Null Controllability for the Heat Equation and Its Consequences for the Time Optimal Control Problem

This page was built for publication: Two Equivalence Theorems of Different Kinds of Optimal Control Problems for Schrödinger Equations