Markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control

We consider the construction of Markov chain approximations for an important class of deterministic control problems. The emphasis is on the construction of schemes that can be easily implemented and which possess a number of highly desirable qualitative properties. The class of problems covered is that for which the control is affine in the dynamics and with quadratic running cost. This class covers a number of interesting areas of application, including problems that arise in large deviations, risk-sensitive and robust control, robust filtering, and certain problems in computer vision. Examples are given as well as a proof of convergence.