Open AccessStabilization of nonautonomous parabolic equations by a single moving actuator
Author(s) -
Behzad Azmi,
Karl Kunisch,
Sérgio S. Rodrigues
Publication year - 2021
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021096
Subject(s) - actuator , concatenation (mathematics) , control theory (sociology) , mathematics , projection (relational algebra) , control (management) , metric (unit) , parabolic partial differential equation , computer science , mathematical analysis , algorithm , differential equation , combinatorics , artificial intelligence , operations management , economics
It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from an oblique projection feedback based on a finite number of static actuators, then we used the continuity of the state when the control varies in a relaxation metric to construct a switching control where at each given instant of time only one of the static actuators is active, finally we construct the moving control by traveling between the static actuators. Numerical computations are performed by a concatenation procedure following a receding horizon control approach. They confirm the stabilizing performance of the moving control.