General stochastic hybrid systems: modelling and optimal control

We develop a model for general stochastic hybrid systems (GSHS) which is a generalization of piecewise-deterministic Markov processes (PDMP), introduced by Davis and stochastic hybrid systems proposed by Hu, Lygeros and Sastry. This model possesses certain desirable properties, as the strong Markov property and the cadlag property. Extending results available for PDMP, we develop the extended generator formula and the differential formula for GSHS. Then we investigate the dynamic programming for GSHS, using the differential formula.