Maximum Principle and Turnpike Properties for Systems with Random Modal Jumps

  • Dean A. Carlson
  • Alain B. Haurie
  • Arie Leizarowitz

Abstract

This chapter deals with a class of stochastic control systems where the random disturbances are stochastic jump processes taking values in a finite set E. Each value iE can be interpreted as a “mode” of the dynamic system. Systems with modal disturbances have been studied in the control literature for a long time in particular in the case of linear dynamics and quadratic performance criterion (e.g. [182]). Here we demonstrate that these processes may be viewed as a sequence of control problems with random stopping time. Each of these problems can be rewritten as a deterministic infinite horizon control system with state and control dependent discount rate. Exploiting this property we first extend the infinite horizon Maximum Principle and some turnpike properties from Chapter 6 to the class of control problems with random stopping time. We conclude by applying these turnpike properties to the case of control systems with random modal jumps.

Keywords

Manifold Assure 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Dean A. Carlson
    • 1
  • Alain B. Haurie
    • 2
  • Arie Leizarowitz
    • 3
  1. 1.Department of MathematicsUniversity of ToledoToledoUSA
  2. 2.Département d’Economie Commerciale et IndustrielleUniversité de GenèveGenèveSuisse
  3. 3.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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