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.
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Borkar, V.S., Ghosh, M.K. & Sahay, P. Optimal Control of a Stochastic Hybrid System with Discounted Cost. Journal of Optimization Theory and Applications 101, 557–580 (1999). https://doi.org/10.1023/A:1021786019871
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DOI: https://doi.org/10.1023/A:1021786019871