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Minimax Control of Discrete-Time Stochastic Systems

This paper gives a unified, self-contained presentation of minimax control problems for discrete-time stochastic systems on Borel spaces, with possibly unbounded costs. The main results include conditions for the existence of minimax strategies for finite-horizon problems and infinite-horizon discounted and undiscounted (average) cost criteria. The results are specialized to control systems with unknown disturbance distributions---also known as games against nature. Two examples illustrate the theory, one of them on the mold level control problem, which is a key problem in the steelmaking industry.