Publication: Limiting discounted-cost control of partially observable stochastic systems
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1999-12
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Abstract
This paper presents two main results on partially observable (PO) stochastic systems. In the first one, we consider a general PO system Xt+1 = F(xt, ~, ~J, Yt = G(xo 'IlJ (t = 0, 1, ... ) (*) on Borel spaces, with possibly unbounded cost-per-stage functions, and give conditions for the existence of a-discount optimal control policies (0 < a < 1). In the second result we specialize (*) to additive-noise systems xt+1 = Fo (Xt' aJ + ~o Yt = Go (xJ + 'Ilt (t= 0, 1, ... ) in Euclidean spaces, with Fn (x,a) and Go(x) converging pointwise to functions F «l(x, a) and G«l(x), respectively, and give conditions for the limiting PO model Xt+1 = F «l(xt, aJ + ~t Yt = G«l(xJ + 'Ilt to have an a-discount optimal policy.
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Partially observable control systems, partially observable Markov control processes, hidden Markov models, discounted cost criterion