Attainable Subspaces and the Bang-Bang Property of Time Optimal Controls for Heat Equations
DOI10.1137/140966022zbMath1330.49022arXiv1404.5096OpenAlexW1994599657MaRDI QIDQ5252500
Yashan Xu, Yubiao Zhang, Gengsheng Wang
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/1404.5096
Optimality conditions for problems involving partial differential equations (49K20) Control/observation systems governed by partial differential equations (93C20) Heat equation (35K05) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Existence theories for optimal control problems involving partial differential equations (49J20) Attainable sets, reachability (93B03) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)
Related Items (16)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Advantages for controls imposed in a proper subset
- Some properties for blowup parabolic equations and their application
- Time optimal boundary controls for the heat equation
- Time optimal controls of the linear Fitzhugh-Nagumo equation with pointwise control constraints
- An observability estimate for the heat equation from a product of two measurable sets
- The bang-bang property of time optimal controls for the Burgers equation
- Observability inequalities and measurable sets
- Note on the cost of the approximate controllability for the heat equation with potential
- 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
- Quantitative unique continuation for the semilinear heat equation in a convex domain
- Semigroups of linear operators and applications to partial differential equations
- Analytic control. I: A priori estimates
- Time optimal problems with Dirichlet boundary controls
- Null and approximate controllability for weakly blowing up semilinear heat equations
- Analysis and control of nonlinear infinite dimensional systems
- An observability estimate for parabolic equations from a measurable set in time and its applications
- Equivalent conditions on periodic feedback stabilization for linear periodic evolution equations
- Quenching time optimal control for some ordinary differential equations
- A time optimal control problem of some linear switching controlled ordinary differential equations
- On the existence of time optimal controls for linear evolution equations
- Time optimal control problems for some non-smooth systems
- 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
- Blowup Time Optimal Control for Ordinary Differential Equations
- Semismooth Newton Methods for Time-Optimal Control for a Class of ODEs
- Approximation of Time Optimal Controls for Heat Equations with Perturbations in the System Potential
- The “Bang-Bang” Principle for the Time-Optimal Problem in Boundary Control of the Heat Equation
- Regularity of the Minimum Time Function and Minimum Energy Problems: The Linear Case
- 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
- Smooth Regularization of Bang-Bang Optimal Control Problems
- A time-optimal boundary controllability problem for the heat equation in a ball
- $L^\infty$-Null Controllability for the Heat Equation and Its Consequences for the Time Optimal Control Problem
- Periodic stabilization for linear time-periodic ordinary differential equations
- Time-Optimal Control of Solutions of Operational Differenital Equations
This page was built for publication: Attainable Subspaces and the Bang-Bang Property of Time Optimal Controls for Heat Equations