Robust null controllability for heat equations with unknown switching control mode

Lu Q, Zuazua E (2014)

Publication Type: Journal article

Publication year: 2014

Journal

Discrete and Continuous Dynamical Systems American Institute of Mathematical Sciences (AIMS)

Book Volume: 34

Pages Range: 4183-4210

Journal Issue: 10

DOI: 10.3934/dcds.2014.34.4183

Abstract

We analyze the null controllability for heat equations in the presence of switching controls. The switching pattern is a priori unknown so that the control has to be designed in a robust manner, based only on the past dynamics, so to fulfill the final control requirement, regardless of what the future dynamics is. We prove that such a robust control strategy actually exists when the switching controllers are located on two non trivial open subsets of the domain where the heat process evolves. Our strategy to construct these robust controls is based on earlier works by Lebeau and Robbiano on the null controllability of the heat equation. It is relevant to emphasize that our result is specific to the heat equation as an extension of a property of finite-dimensional systems that we fully characterize but that it may not hold for wave-like equations.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Sichuan University (SCU) / 四川大学 CN China (CN) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Lu, Q., & Zuazua, E. (2014). Robust null controllability for heat equations with unknown switching control mode. Discrete and Continuous Dynamical Systems, 34(10), 4183-4210. https://dx.doi.org/10.3934/dcds.2014.34.4183

MLA:

Lu, Qi, and Enrique Zuazua. "Robust null controllability for heat equations with unknown switching control mode." Discrete and Continuous Dynamical Systems 34.10 (2014): 4183-4210.

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