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

Franco Pedro; Schaum A.; Bernal Jaquez Roberto

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

机译：受限空间中具有任意势的Schroedinger方程的Backstepping控制

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In this work the control design problem for the Schrodinger 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 Poschl-Teller potentials as well as the semilinear Schrodinger equation with cubic potential.

机译：在这项工作中，解决了具有任意电位的薛定inger方程的控制设计问题。特别地，设计了一种控制器，该控制器（i）对于与空间有关的电势将状态概率密度函数转向给定的解，并且（ii）对于与空间和状态有关的电势将指数解稳定为零。使用后推控制器解决了该问题，该控制器将初始概率波函数和目标概率波函数之间的偏差控制为零。严格建立了指数收敛性，并使用数值模拟对Morse和Poschl-Teller势以及具有三次势的半线性Schrodinger方程进行了说明。

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《Mathematical Problems in Engineering》 |2018年第9期|1826783.1-1826783.9|共9页
作者
Franco Pedro; Schaum A.; Bernal Jaquez Roberto;
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Univ Kiel, Chair Automat Control, Kiel, Germany;

Univ Autonoma Metropolitana Cuajimalpa, Posgrad Ciencias Nat & Ingn, Mexico City, DF, Mexico;

Univ Autonoma Metropolitana Cuajimalpa, Dept Matemat Aplicadas & Sistemas, Mexico City, DF, Mexico;

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1. Backstepping Control for the Schrödinger Equation with an Arbitrary Potential in a Confined Space [J] . Pedro Franco, A. Schaum, Roberto Bernal Jaquez Mathematical Problems in Engineering: Theory, Methods and Applications . 2018,第a期

机译：SCHR＆＃XF6的BackStepping控制; Dinger方程在一个受限空间中的任意潜力
2. THE NONLINEAR SCHROEDINGER EQUATIONS WITH HARMONIC POTENTIAL IN MODULATION SPACES [J] . Bhimani Divyang G. Discrete and continuous dynamical systems . 2019,第10期

机译：调制空间中具有调和势的非线性Schroedinger方程
3. On a Class of Nonlinear Schroedinger Equations with Nonnegative Potentials in Two Space Dimensions [J] . Jian Zhang, Ji Shu Mathematical notes . 2012,第3a4期

机译：关于二维空间上具有非负势的一类非线性Schroedinger方程
4. On the Inversion of Schroedinger's Equation for Periodic Potentials: Dynamical Ptychography [C] . International centennial symposium on the electron . 1998

机译：关于周期电位的施罗德格方程的反演：动态PTYCHOGA
5. On the existence of infinite bump solutions of nonlinear Schroedinger equations with periodic potentials [D] . Thandi, Neeza. 1995

机译：具有周期性潜力的非线性施格格方程无限凸块解的存在
6. Separation of the Variables in the One-Particle Schroedinger Equation in 3-Space [O] . Luther Pfahler Eisenhart 1949

机译：一维Schroedinger方程在3维空间中的变量分离
7. Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach [O] . Coron, Jean-Michel, Nguyen, Hoai-Minh 2015

机译：一维空间变系数热方程的反步法的可控性和有限时间稳定
8. Schroedinger Equation for Central Power Law Potentials and the Classical Theory of Ordinary Linear Differential Equations of the Second Order [R] . Lima, M. L., Mignaco, J. A. 1985

机译：中心幂律势的schroedinger方程与二阶常微分线性微分方程的经典理论

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

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