Stability of the Barto-Sutton Network under Rational Control Orbits

The class of networks based on the Barto-Sutton architecture are known to be capable of solving complex, multi-dimensional control problems. In these problems, the objective of the task is the localization of a system within a contiguous region of its state space. In this work, asymptotic stability criteria are derived for the Adaptive Critical Element (ACE) of the network. Here, the weights of the network are viewed as the state of a linear time-variant state- space learning machine. For system trajectories which can be represented by simple rational polynomials, discrete-time techniques are used to analyze the stability of the learning machine. The advantages of this approach are that it both provides bounds for the learning parameters and characterizes the resultant learning behavior.