Journal of Optimization Theory and Applications

, Volume 101, Issue 3, pp 557–580

Optimal Control of a Stochastic Hybrid System with Discounted Cost

  • V. S. Borkar
  • M. K. Ghosh
  • P. Sahay
Article

DOI: 10.1023/A:1021786019871

Cite this article as:
Borkar, V.S., Ghosh, M.K. & Sahay, P. Journal of Optimization Theory and Applications (1999) 101: 557. doi:10.1023/A:1021786019871

Abstract

We address the optimal control problem of a very general stochastic hybrid system with both autonomous and impulsive jumps. The planning horizon is infinite and we use the discounted-cost criterion for performance evaluation. Under certain assumptions, we show the existence of an optimal control. We then derive the quasivariational inequalities satisfied by the value function and establish well-posedness. Finally, we prove the usual verification theorem of dynamic programming.

Hybrid systemsswitching diffusionsautonomous jumpsimpulsive jumpsdiscounted costoptimal control

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • V. S. Borkar
    • 1
  • M. K. Ghosh
    • 2
  • P. Sahay
    • 3
  1. 1.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  3. 3.Department of MathematicsIndian Institute of ScienceBangaloreIndia