State Dependent Jump Models in Optimal Control

Models of linear and nonlinear optimal control applications are considered in which random discrete jumps in the system are state dependent in both rate and amplitude. These discrete jumps are treated as a Poisson processes in continuous time. This type of random noise allows for greater realism while modeling industrial and natural phenomena in which important changes occur with jumps. Modeling concerns are described and the appropriate modifications are indicated for numerically solving the resulting optimal control problems. Applications to a multistage manufacturing system and to the management of a natural resource under stochastic price fluctuations are used to illustrate this type of dynamical formulation.