Journal of Optimization Theory and Applications

, Volume 101, Issue 3, pp 557–580

Optimal Control of a Stochastic Hybrid System with Discounted Cost

Authors

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