Finite-Horizon Problems

Abstract

In this chapter, we consider the Markov control model

$$ (X,A,\{ A(x)|x \in X\} ,Q,c), $$

(3.1.1)

introduced in Definition 2.2.1, and the control problem we are interested in is to minimize the finite-horizon performance criterion

$$ J(\pi ,x): = E_x^\pi \left[ {\sum\limits_{t = 0}^{N - 1} {c({x_t},{a_t}) + {c_N}({x_N})} } \right], $$

(3.1.2)

with c _N , the terminal cost function, a given measurable function on X.