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- Title
Backstepping Control for the Schrödinger Equation with an Arbitrary Potential in a Confined Space.
- Authors
Franco, Pedro; Schaum, A.; Jaquez, Roberto Bernal
- 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.
- Subjects
SCHRODINGER equation; CONFINED spaces (Work environment); PROBABILITY density function; WAVE functions; COMPUTER simulation
- Publication
Mathematical Problems in Engineering, 2018, p1
- ISSN
1024-123X
- Publication type
Article
- DOI
10.1155/2018/1826783