Numerical methods for stochastic control problems in continuous time
SIAM Journal on Control and Optimization
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Journal of Optimization Theory and Applications
Hierarchical decision making in stochastic manufacturing systems
Hierarchical decision making in stochastic manufacturing systems
Asymptotic expansions of singularly perturbed systems involving rapidly fluctuating Markov chains
SIAM Journal on Applied Mathematics
Continuous-time Markov chains and applications: a singular perturbation approach
Continuous-time Markov chains and applications: a singular perturbation approach
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This work develops Markov chain approximation techniques for a class of nonlinear control problems in which the dynamics are given by ordinary differential equations involving a finite-state Markov chain. Our motivation comes from production planning and controls of various manufacturing systems with unreliable machines. An algorithm for the optimal control problem is developed. Our main effort is to prove the desired convergence properties of the method for approximating the optimal control and the value function via Markov chain approximation techniques. It is shown that the sequence of approximating Markov chain converges to that of the system under consideration and that the sequence of approximating value functions converges to the true value function.