Stochastic optimal control of dynamic systems under Gaussian and poisson excitations

A mathematical pendulum under Poisson and Gaussian excitations is considered. A bounded in magnitude control force is applied to the system in order to minimize mean system´s response energy. An optimal control law for the Boltza cost function may be found via Dynamic Programming approach, resulting in the Hamilton-Jacobi-Bellman (HJB) equation. Solution to the nonlinear HJB equation has been derived in two steps, as suggested by the recently introduced method of Hybrid Solution. Influence of viscous damping on synthesis of an optimal control law is investigated.