Backstepping Control for the Schrödinger Equation with an Arbitrary Potential in a Confined Space
Joint Authors
Franco, Pedro
Schaum, A.
Bernal Jaquez, Roberto
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-07-19
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
In this work the control design problem for the Schrödinger equation with an arbitrary potential is addressed.
In particular a controller is designed which (i) for a space-dependent potential steers the state probability density function to a prescribed solution and (ii) for a space and state-dependent potential exponentially stabilizes the zero solution.
The problem is addressed using a backstepping controller that steers to zero the deviation between the initial probability wave function and the target probability wave function.
The exponential convergence property is rigorously established and the convergence behavior is illustrated using numerical simulations for the Morse and the Pöschl-Teller potentials as well as the semilinear Schrödinger equation with cubic potential.
American Psychological Association (APA)
Franco, Pedro& Schaum, A.& Bernal Jaquez, Roberto. 2018. Backstepping Control for the Schrödinger Equation with an Arbitrary Potential in a Confined Space. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1205856
Modern Language Association (MLA)
Franco, Pedro…[et al.]. Backstepping Control for the Schrödinger Equation with an Arbitrary Potential in a Confined Space. Mathematical Problems in Engineering No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1205856
American Medical Association (AMA)
Franco, Pedro& Schaum, A.& Bernal Jaquez, Roberto. Backstepping Control for the Schrödinger Equation with an Arbitrary Potential in a Confined Space. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1205856
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1205856