Approximate Inverse-Dynamics based Robust Control using Static and Dynamic State Feedback
Applications of Neural Adaptive Control Technology, World Scientific, Singapore, (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 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.