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Dynamic Programming Equations

  • Harold J. Kushner
  • Paul G. Dupuis
Part of the Applications of Mathematics book series (SMAP, volume 24)

Abstract

In this chapter we define many of the standard control problems whose numerical solutions will concern us in the subsequent chapters. Other, less familiar control problems will be discussed separately in later chapters. We will first define cost functionals for uncontrolled processes, and then formally discuss the partial differential equations which they satisfy. Then the cost functionals for the controlled problems will be stated and the partial differential equations for the optimal cost formally derived. These partial differential equations are generally known as Bellman equations or dynamic programming equations. The main tool in the derivations is Itô’s formula.

Keywords

Average Cost Regular Point Optimal Cost Admissible Control Bellman Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Harold J. Kushner
    • 1
  • Paul G. Dupuis
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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