The Deterministic Stochastic Transition in Control Processes and the Use of Maximum and Integral Transforms

Abstract

Consider the "minimum transform" Phi(y) of a function F(x) defined by (1.1) Phi(y) = min [F(x) - xy]. Then, under certain conditions on F, the essential one being that of convexity, the inverse relation is simply (1.2) F(x) = max [Phi(y) + xy], that is, F is the "maximum transform" of Phi. We shall refer to transforms of either type generically as "maximum transforms." In this paper we shall show that use of the transform leads to a very natural treatment of certain control problems. The pair of relations (1.1), (1.2) is strikingly analogous in form to a Fourier integral transformation and its inversion.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1967
Accession Number
AD1027238

Entities

People

  • P Whittle

Organizations

  • University of Manchester

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Air Force
  • Boundaries
  • Computer Programming
  • Dynamic Programming
  • Equations
  • Fourier Transformation
  • Integral Transforms
  • Integrals
  • Inversion
  • Military Research
  • Physical Sciences
  • Probability
  • Scientific Research
  • Stochastic Control
  • Terminals
  • Test And Evaluation
  • Transitions

Fields of Study

  • Mathematics

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  • Analytical Mechanics
  • Image Processing and Computer Vision.
  • Mathematical Modeling and Probability Theory.