Constrained bilinear systems

Navin Khaneja; Steffen J. Glaser

Constrained bilinear systems

Navin Khaneja, Steffen J. Glaser

Associate Professorship of Organic Chemistry

Broad Institute of Harvard University

Research output: Contribution to journal › Conference article › peer-review

3 Scopus citations

Abstract

In this paper, we study some model control problems which arise in connection with optimal manipulation of dissipative quantum dynamics. It is shown that the problem of optimal control of quantum mechanical phenomenon in presence of dissipation can be reduced to the study of optimization problems associated with a class of constrained Bilinear control systems. These Bilinear systems ẋ = (A + Σ_nⁿ u_iB_i)x are characterized by the fact that the controls can be expressed as polynomial functions of fewer parameters, i.e. u_i = g_i(v₁, v₂,..., v_k) where g_i are polynomials and k < n. A general study of these systems is expected to find immediate applications in coherent control of quantum mechanical phenomenon.

Original language	English
Pages (from-to)	51-56
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	1
State	Published - 2002
Event	41st IEEE Conference on Decision and Control - Las Vegas, NV, United States Duration: 10 Dec 2002 → 13 Dec 2002

Cite this

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title = "Constrained bilinear systems",

abstract = "In this paper, we study some model control problems which arise in connection with optimal manipulation of dissipative quantum dynamics. It is shown that the problem of optimal control of quantum mechanical phenomenon in presence of dissipation can be reduced to the study of optimization problems associated with a class of constrained Bilinear control systems. These Bilinear systems ẋ = (A + Σnn uiBi)x are characterized by the fact that the controls can be expressed as polynomial functions of fewer parameters, i.e. ui = gi(v1, v2,..., vk) where gi are polynomials and k < n. A general study of these systems is expected to find immediate applications in coherent control of quantum mechanical phenomenon.",

author = "Navin Khaneja and Glaser, {Steffen J.}",

year = "2002",

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journal = "Proceedings of the IEEE Conference on Decision and Control",

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note = "41st IEEE Conference on Decision and Control ; Conference date: 10-12-2002 Through 13-12-2002",

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AU - Khaneja, Navin

AU - Glaser, Steffen J.

PY - 2002

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N2 - In this paper, we study some model control problems which arise in connection with optimal manipulation of dissipative quantum dynamics. It is shown that the problem of optimal control of quantum mechanical phenomenon in presence of dissipation can be reduced to the study of optimization problems associated with a class of constrained Bilinear control systems. These Bilinear systems ẋ = (A + Σnn uiBi)x are characterized by the fact that the controls can be expressed as polynomial functions of fewer parameters, i.e. ui = gi(v1, v2,..., vk) where gi are polynomials and k < n. A general study of these systems is expected to find immediate applications in coherent control of quantum mechanical phenomenon.

AB - In this paper, we study some model control problems which arise in connection with optimal manipulation of dissipative quantum dynamics. It is shown that the problem of optimal control of quantum mechanical phenomenon in presence of dissipation can be reduced to the study of optimization problems associated with a class of constrained Bilinear control systems. These Bilinear systems ẋ = (A + Σnn uiBi)x are characterized by the fact that the controls can be expressed as polynomial functions of fewer parameters, i.e. ui = gi(v1, v2,..., vk) where gi are polynomials and k < n. A general study of these systems is expected to find immediate applications in coherent control of quantum mechanical phenomenon.

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M3 - Conference article

AN - SCOPUS:0036996395

SN - 0191-2216

VL - 1

SP - 51

EP - 56

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - 41st IEEE Conference on Decision and Control

Y2 - 10 December 2002 through 13 December 2002

ER -

Constrained bilinear systems

Abstract

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