Control of Heat Equation with Actuator Placement

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


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
Link to Google Scholar
). Its goal is to choose a place to apply an actuator in a given area depending on time. We consider a rectangle \Omega=[0,1]\times[0,2] with the boundary \partial\Omega 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--323Link to Google Scholar