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Iterative method for optimal control problems for Markov chains, discussing degenerate nonlinear elliptic equations solution in optimal stochastic control theory
Optimal control problems for Markov chains solved by iterative method, using nonlinear finite difference equations to approximate degenerate elliptic functions
Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.