scholarly journals Time optimal control of the heat equation with pointwise control constraints

2013 ◽  
Vol 19 (2) ◽  
pp. 460-485 ◽  
Author(s):  
Karl Kunisch ◽  
Lijuan Wang
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Time Optimal Control ◽  
Control Constraints ◽  
Time Optimal ◽  
Pointwise Control Constraints

A time-optimal boundary controllability problem for the heat equation in a ball

2014 ◽  
Vol 144 (6) ◽  
pp. 1171-1189 ◽  
Author(s):  
Sorin Micu ◽  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Parabolic Type ◽  
Time Optimal Control ◽  
Main Ingredient ◽  
Controllability Problem ◽  
Boundary Controllability ◽  
Müntz Polynomials ◽  
Time Optimal ◽  
Dimensional Ball

The aim of this paper is to study a boundary time-optimal control problem for the heat equation in a two-dimensional ball. The main ingredient is the extension of a result concerning Müntz polynomials due to Borwein and Erdélyi that allows us to prove an observability inequality for the dynamical system's truncation to a finite number of modes. This result, combined with a well-known Lebeau–Robbiano argument used to show the null-controllability of parabolic type equations, enables us to deduce the existence, uniqueness and bang-bang properties for the boundary time-optimal control.

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