### Abstract

We show that a corollary of a local approximate controllability result for the bilinear rod equation in [1] is that the controls which "steer" the modes of the rod equation also move the modes of a controlled Schrödinger equation. Specifying a target point for the Schrödinger system restricts but does not determine the outcome of the controlled rod equation. The local result is a special case of a general local result for hyperbolic systems, which is used in [1] to obtain a global approximate controllability result. After modifying the latter, we obtain a global result for the two systems.

Original language | English (US) |
---|---|

Pages (from-to) | 301-306 |

Number of pages | 6 |

Journal | Systems and Control Letters |

Volume | 24 |

Issue number | 4 |

DOIs | |

State | Published - Mar 10 1995 |

### Fingerprint

### Keywords

- Bilinear control
- Local control
- Phase shift
- Rod equation
- Schrödinger equation

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science(all)
- Mechanical Engineering
- Electrical and Electronic Engineering

### Cite this

**Simultaneous control of a rod equation and a simple Schrödinger equation.** / Kime, K.

Research output: Contribution to journal › Article

*Systems and Control Letters*, vol. 24, no. 4, pp. 301-306. https://doi.org/10.1016/0167-6911(94)00022-N

}

TY - JOUR

T1 - Simultaneous control of a rod equation and a simple Schrödinger equation

AU - Kime, K.

PY - 1995/3/10

Y1 - 1995/3/10

N2 - We show that a corollary of a local approximate controllability result for the bilinear rod equation in [1] is that the controls which "steer" the modes of the rod equation also move the modes of a controlled Schrödinger equation. Specifying a target point for the Schrödinger system restricts but does not determine the outcome of the controlled rod equation. The local result is a special case of a general local result for hyperbolic systems, which is used in [1] to obtain a global approximate controllability result. After modifying the latter, we obtain a global result for the two systems.

AB - We show that a corollary of a local approximate controllability result for the bilinear rod equation in [1] is that the controls which "steer" the modes of the rod equation also move the modes of a controlled Schrödinger equation. Specifying a target point for the Schrödinger system restricts but does not determine the outcome of the controlled rod equation. The local result is a special case of a general local result for hyperbolic systems, which is used in [1] to obtain a global approximate controllability result. After modifying the latter, we obtain a global result for the two systems.

KW - Bilinear control

KW - Local control

KW - Phase shift

KW - Rod equation

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=0029271067&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029271067&partnerID=8YFLogxK

U2 - 10.1016/0167-6911(94)00022-N

DO - 10.1016/0167-6911(94)00022-N

M3 - Article

AN - SCOPUS:0029271067

VL - 24

SP - 301

EP - 306

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 4

ER -