Stochastic control with -dependent noise: Finite horizon case

Abstract: In this paper, the finite horizon mixed control problem is studied for the systems governed by Itô-type nonlinear stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the mixed control under consideration is associated with the four cross-coupled Hamilton–Jacobi equations. A discrete approximation algorithm is presented for solving the coupled generalized differential Riccati equations arising from linear stochastic control. A necessary condition and a sufficient condition for the existence of the finite horizon stochastic control are derived. In particular, some previous results on deterministic and stochastic control can be viewed as corollaries of our main theorems. [Copyright &y& Elsevier]