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