Control of Heat Equation with Actuator Placement: Difference between revisions

Control of Heat Equation with Actuator Placement
State dimension:	1
Differential states:	3
Discrete control functions:	1
Interior point equalities:	3

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Revision as of 15:02, 23 February 2016

This problem is governed by the heat equation and is adapted from Iftime and Demetriou ([Iftime2009]Author: Orest V. Iftime; Michael A. Demetriou
Journal: {A}utomatica
Number: 2
Pages: 312--323
Title: {O}ptimal control of switched distributed parameter systems with spatially scheduled actuators
Volume: 45
Year: 2009
). Its goal is to choose a place to apply an actuator in a given area depending on time. We consider a rectangle $Ω = [0, 1] \times [0, 2]$ with the boundary $\partial Ω$ and the time horizon $T = [0, 10]$ as the domains. The objective function is quadratic, its first term captures the desired final state $\bar{u} \equiv 0$ , the second term regularize the state over time and the third term regularize the continuous controls. The constraints are a source budget, which limits the quantity of placed actuators, and the two-dimensional heat equation with some source function. Additionally, we assume Dirichlet boundary conditions and initial conditions.

Mathematical formulation

Parameters

Reference solution

Source Code

References

[Iftime2009]

Orest V. Iftime; Michael A. Demetriou (2009): {O}ptimal control of switched distributed parameter systems with spatially scheduled actuators . {A}utomatica, 45, 312--323

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+This problem is governed by the heat equation and is adapted from Iftime and Demetriou (<bib id="Iftime2009"/>).
+Its goal is to choose a place to apply an actuator in a given area depending on time.
+We consider a rectangle <math>\Omega=[0,1]\times[0,2]</math> with the boundary <math>\partial\Omega</math> and the time horizon <math>T=[0,10]</math> as the domains.
+The objective function is quadratic, its first term captures the desired final state <math>\bar{u}\equiv 0</math>, the second term regularize the state over time and the third term regularize the continuous controls.
+The constraints are a source budget, which limits the quantity of placed actuators, and the two-dimensional heat equation with some source function.
+Additionally, we assume Dirichlet boundary conditions and initial conditions.