Controllability Under Positivity Constraints of Multi-d Wave Equations
Pighin D, Zuazua E (2019)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2019
Publisher: Springer International Publishing
Edited Volumes: Trends in Control Theory and Partial Differential Equations
Series: Springer INdAM Series
Book Volume: 32
Pages Range: 195-232
ISBN: 978-3-030-17949-6
DOI: 10.1007/978-3-030-17949-6_11
Abstract
We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class of wave equations with time-independent coefficients. According to it, the system can be driven from a steady state generated by a strictly positive control to another, by means of nonnegative controls, and provided the time of control is long enough. Secondly, under the added assumption of conservation and coercivity of the energy, controllability is proved between states lying on two distinct trajectories. Our methods are described and developed in an abstract setting, to be applicable to a wide variety of control systems.
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APA:
Pighin, D., & Zuazua, E. (2019). Controllability Under Positivity Constraints of Multi-d Wave Equations. In Fatiha Alabau-Boussouira, Fabio Ancona, Alessio Porretta, Carlo Sinestrari (Eds.), Trends in Control Theory and Partial Differential Equations. (pp. 195-232). Springer International Publishing.
MLA:
Pighin, Dario, and Enrique Zuazua. "Controllability Under Positivity Constraints of Multi-d Wave Equations." Trends in Control Theory and Partial Differential Equations. Ed. Fatiha Alabau-Boussouira, Fabio Ancona, Alessio Porretta, Carlo Sinestrari, Springer International Publishing, 2019. 195-232.
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