On Variable-Structure Stochastic Automata

A stochastic automaton with a variable structure (SAVS) may be described by the sextuple {X, Φ, α, p, U, G} where X={x0, x1,⋯,xk} is the input set, Φ = {Φ1, Φ2,⋯,Φs} is the internal state set, α = {α1, α1,⋯,αr} with r ≤ s is the output or action set, p is the state probability vector (i.e., at stage or time instant n, p(n) = (p1(n), p2(n),⋯,ps(n)) governing the choice of the state, U is an updating scheme which generates p(n + 1) from p(n) and G:Φ → α is the output function. In general, G may be a stochastic function. In this paper it is assumed that G is deterministic and one-to-one (i.e., r = s), k = 1 and s < ∞.