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A Separation theorem for expected value and feared value discrete time control. (English) Zbl 0878.93062

This work is built upon Maslov’s idempotent measure theory. More specifically, this paper contains interesting applications of the parallelism between probability and cost measures introduced independently by Del Moral and Quadrat.
The main purpose is to show how to use these tools to give a treatment of minimax control problems completely parallel to that of stochastic control. The author improves his earlier work and proposes a complete parallel between minimax and stochastic separation theorems.
This study is self-contained and proposes a very convenient way of understanding the connections between minimax and stochastic control problems.

MSC:

93E20 Optimal stochastic control
90C40 Markov and semi-Markov decision processes
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References:

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