Topology of classical molecular optimal control landscapes for multi-target objectives

Abstract

This paper considers laser-driven optimal control of an ensemble of non-interacting molecules whose dynamics lie in classical phase space. The molecules evolve independently under control to distinct final states. We consider a control landscape defined in terms of multi-target (MT) molecular states and analyze the landscape as a functional of the control field. The topology of the MT control landscape is assessed through its gradient and Hessian with respect to the control. Under particular assumptions, the MT control landscape is found to be free of traps that could hinder reaching the objective. The Hessian associated with an optimal control field is shown to have finite rank, indicating an inherent degree of robustness to control noise. Both the absence of traps and rank of the Hessian are shown to be analogous to the situation of specifying multiple targets for an ensemble of quantum states. Numerical simulations are presented to illustrate the classical landscape principles and further characterize the system behavior as the control field is optimized.

Document Details

Document Type
Pub Defense Publication
Publication Date
Apr 20, 2015
Source ID
10.1063/1.4918274

Entities

People

  • Carlee Joe-Wong
  • Herschel A. Rabitz
  • Re-Bing Wu
  • Tak-san Ho

Organizations

  • Army Research Office
  • National Natural Science Foundation of China
  • National Science Foundation
  • Princeton University
  • Tsinghua University

Tags

Readers

  • Joint Military Operations and Doctrine.
  • Linear Algebra
  • Wetland-Land-Environmental Management.

Technology Areas

  • Directed Energy
  • Quantum Computing
  • Quantum Science - Quantum Dots
  • Space
  • Space - Spacecraft Maneuvers