Approximate inverse-dynamics based robust control using static and dynamic feedback
Cs. Szepesvári and A. Lõrincz
Neural Adaptive Control Theory II.
in press (1997)
Abstract
It is rigorously shown that inverse-dynamics models
can be used to stabilize plants of any order
provided that the inverse-dynamic model is used in a mixed
mode fashion, in that of a `Static and Dynamic' State-feedback (SDS)
mode. When the resulting controller is
used for tracking increasing the gain of the dynamic
feedback decreases the tracking error. Yet another attractive
feature of the SDS scheme is that the inverse-dynamics
model can be tuned on-line by {\em any} adaptation mechanism
without cancelling stability if the conditions of the
non-adaptive stability theorem hold at any time instant.
Computer simulations of the control of a chaotic
bioreactor and a `realistic' robotic manipulator
demonstrate the robustness of the approach.
It is shown that SDS control will yield
zero asymptotic error when controlling the bioreactor
using an inverse-dynamics model which when used in a
traditional mode would yield intolerably large errors. In
the case of the robotic arm simulations the effects of perturbation
and sampling frequency are investigated and the SDS control is
compared with the non-adaptive computed torque method.
A fully self-organizing associative neural network
architecture that can be used to
approximate the inverse-dynamics in the
form of a Position-and-Direction-to-Action (PDA) map is
also described. Similarities between the basal ganglia -- thalamocortical
loops and the SDS scheme are discussed and it is argued that the SDS
scheme could be viewed as a model of higher order motor functions
of these areas.
