toggle visibility Search & Display Options

Select All    Deselect All
 |   | 
Details
   print
  Record Links
Author Contreras, M.; Pellicer, R.; Villena, M. pdf  doi
openurl 
  Title Dynamic optimization and its relation to classical and quantum constrained systems Type Journal Article
  Year 2017 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A  
  Volume 479 Issue Pages 12-25  
  Keywords Dynamic optimization; Constrained systems; Dirac's method; Quantum mechanics  
  Abstract We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop lambda-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Psi (x, t) = e(is(x,t)) in the quantum Schrodinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x, t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem. (C) 2017 Elsevier B.V. All rights reserved.  
  Address [Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo] Univ Adolfo Ibanez, Fac Engn & Sci, Santiago, Region Metropol, Chile, Email: mauricio.contreras@uai.cl  
  Corporate Author Thesis  
  Publisher Elsevier Science Bv Place of Publication (up) Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0378-4371 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000400213800002 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 731  
Permanent link to this record
Select All    Deselect All
 |   | 
Details
   print

Save Citations:
Export Records: