Backstepping Control for the Schrödinger Equation with an Arbitrary Potential in a Confined Space

Pedro Franco, A. Schaum and Roberto Bernal Jaquez

Mathematical Problems in Engineering, 2018, vol. 2018, 1-9

Abstract:

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.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2018/1826783.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2018/1826783.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:1826783

DOI: 10.1155/2018/1826783

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().