Distal Learning for Inverse Modelling of Dynamical Systems

This paper addresses stability issues of the learning process when the distal in space approach (Jordan & Rumelhart 92) is used to learn inverse models of dynamical systems. Both direct and indirect versions of command error approximations are analysed on linear plants. It is shown that none of them is suitable when the plant is an unstable non-minimum phase system. When the plant is unstable, an additional problem must be solved: stability of the control system must be guaranteed at the beginning of the learning process. We then propose solutions for the case where direct version is applied to non-minimum phase stable plants. These solutions are compared on a simulated problem. Extensions of these methods to nonlinear systems are also discussed.