Distal Learning for Inverse Modeling of Dynamical Systems

This paper addresses stability issues of the learning process when the distal-in-space approach is used to learn inverse models of dynamical systems. Both direct and indirect versions of this approach are analysed for 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 do not deal with this additional problem but concentrate on the stability and the speed of the learning process. We propose solutions in the case of the direct version, applied to non-minimum phase stable plants. These solutions are compared on a linear plant control problem. Extensions to nonlinear systems are briefly discussed.