Optimality of “full bang to reduce predicted miss” for some partially observed stochastic control problems
For final value stochastic control problems, the “predicted miss” of the title is the expected final position, conditional on the cumulative information to date, if no further control is exerted. For partially observed problems with bounded control, similar to some proposed by Åström, we use PDE methods to show that predicted miss defines the switching surfaces for an optimal “bang-bang” control law whose gist, simply stated, is to reduce predicted miss. The surfaces in question are explicitly calculated.
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