Limiting discounted-cost control of partially observable stochastic systems

Summary form only given. The paper presents two main results on partially observable (PO) stochastic systems. In the first one, we consider a general PO system x_t+1=F(_xt, a_t , ξ_t), y_t=G(_xt, η_t ) (t=0, 1,...) on Borel spaces, with possibly unbounded cost-per-stage functions, and give conditions for the existence of α-discount optimal control policies (0<α<1). In the second result we specialize (1) to additive-noise systems x_t+1=F_n(_xt, a_t)+ξ_t , y_t=G_n(_xt)+η_t (t=0, 1,...) in Euclidean spaces, with F_n(x, a) and G_n (x) converging pointwise to functions F_∞(x, a) and G_∞(x), respectively, and give conditions for the limiting PO model x_t+1=F_∞(_xt, a _t)+ξ_t, y_t=G_∞(_x t)+η_t to have an α-discount optimal policy