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Linear convex stochastic control problems over an infinite horizon

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1 Author(s)
Bertsekas, D.P. ; Stanford University, Stanford, CT, USA

A stochastic control problem over an infinite horizon which involves a linear system and a convex cost functional is analyzed. We prove the convergence of the dynamic programming algorithm associated with the problem, and we show the existence of a stationary Borel measurable optimal control law. The approach used illustrates how results on infinite time reachability [1] can be used for the analysis of dynamic programming algorithms over an infinite horizon subject to state constraints.

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Automatic Control, IEEE Transactions on  (Volume:18 ,  Issue: 3 )