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Title: Fast cooling for a system of stochastic oscillators

We study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired steady state corresponding to reduced thermal noise. Among the feedback controls achieving the desired asymptotic transfer, we find that the most efficient one from an energy point of view is characterized by time-reversibility. We also extend the theory of Schrödinger bridges to this model, thereby steering the system in finite time and with minimum effort to a target steady-state distribution. The system can then be maintained in this state through the optimal steady-state feedback control. The solution, in the finite-horizon case, involves a space-time harmonic function φ, and −logφ plays the role of an artificial, time-varying potential in which the desired evolution occurs. This framework appears extremely general and flexible and can be viewed as a considerable generalization of existing active control strategies such as macromolecular cooling. In the case of a quadratic potential, the results assume a form particularly attractive from the algorithmic viewpoint as the optimal control can be computed via deterministic matricial differential equations. An example involving inertial particles illustrates both transient and steady state optimal feedback control.
Authors:
;  [1] ;  [2]
  1. Department of Electrical and Computer Engineering, University of Minnesota, 200 Union Street S.E., Minneapolis, Minnesota 55455 (United States)
  2. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova (Italy)
Publication Date:
OSTI Identifier:
22479557
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; COOLING; DIFFERENTIAL EQUATIONS; FEEDBACK; OPTIMAL CONTROL; OSCILLATORS; STEADY-STATE CONDITIONS; STOCHASTIC PROCESSES; TRANSIENTS