Journal of Optimization Theory and Applications

, Volume 101, Issue 3, pp 557-580

First online:

Optimal Control of a Stochastic Hybrid System with Discounted Cost

  • V. S. BorkarAffiliated withDepartment of Computer Science and Automation, Indian Institute of Science
  • , M. K. GhoshAffiliated withDepartment of Mathematics, Indian Institute of Science
  • , P. SahayAffiliated withDepartment of Mathematics, Indian Institute of Science

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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 systems switching diffusions autonomous jumps impulsive jumps discounted cost optimal control