Control of Heat Equation with Actuator Placement
Control of Heat Equation with Actuator Placement | |
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State dimension: | 1 |
Differential states: | 1 |
Continuous control functions: | |
Discrete control functions: | |
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
).
Its goal is to choose a place to apply an actuator in a given area depending on time.
We consider a rectangle with the boundary and the time horizon as the domains.
The objective function is quadratic, its first term captures the desired final state , 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 |