Optimal boundary control of the heat equation with target function at terminal time.
type: Item
instance of: scholarly article
title: Optimal boundary control of the heat equation with target function at terminal time.
zbMATH Open document ID: 1040.49037
DOI: 10.1016/S0096-3003(01)00011-X
author: Guangcao Ji
author: Clyde Martin
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The paper considers the problem of minimizing the functional \[ I= \int_\Omega| y(T, x)- h(x)|^2\,dx+ \int^T_0 \int_{\partial\Omega}| u(t,x)|^2\,dS\,dt \] subject to \[ \begin{gathered} y_t=\Delta y\quad\text{in }(0,T)\times \Omega,\quad y(0,\cdot)= y_0(\cdot),\\ y(t, x)= u(t,x)\quad\text{on }(0,T)\times \partial\Omega,\end{gathered} \] where \(\Omega\subset\mathbb{R}^2\) is a Lipschitz domain with boundary \(\partial\Omega\), \(y_0\) and \(h\) are given functions. The authors reformulate the original problem as an abstract one, derive the optimality system and obtain the optimal feedback by using the formal solution of the corresponding Riccati equation.
Mathematics Subject Classification ID: 49N35
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35B37
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 49K20
zbMATH DE Number: 1861049
zbMATH Keywords: optimal control
zbMATH Keywords: parabolic equation
zbMATH Keywords: feedback control
reviewed by: Uldis Raitums
MaRDI profile type: Publication
cites work: Q4721455
cites work: Partially observed analytic systems with fully unbounded actuators and sensors-FEM algorithms
cites work: Dirichlet Boundary Control Problem for Parabolic Equations with Quadratic Cost: Analyticity and Riccati’s Feedback Synthesis
cites work: Riccati Differential Equations with Unbounded Coefficients and Nonsmooth Terminal Condition—The Case of Analytic Semigroups
cites work: Differential and algebraic Riccati equations with application to boundary/point control problems: Continuous theory and approximation theory
cites work: Optimal control, statistics and path planning
cites work: Q4000368
cites work: Semigroups of linear operators and applications to partial differential equations
full work available at URL: s0096-3003(01)00011-x
OpenAlex ID: W1990722185
Recommended article: Time optimal boundary controls for the heat equation
Recommended article: Optimal boundary control of a hyperbolic system of heat equations
Recommended article: Об одной задаче оптимального управления для уравнения теплопроводности с интегральным граничным условием
Recommended article: Optimal boundary control of heat conduction problems on an infinite time domain by control parameterization
Recommended article: Time and norm optimal controls for the heat equation with dynamical boundary conditions
Recommended article: Q3479098
Recommended article: Exact boundary controllability for heat equation with time dependent coefficients
Recommended article: Time optimal control of the heat equation with pointwise control constraints
Recommended article: Q4218354
Recommended article: On the Reachable States for the Boundary Control of the Heat Equation
description: scientific article; zbMATH DE number 1861049