Gaussian networks for direct adaptive control

TLDR

The paper proposes a direct adaptive tracking control architecture for continuous‑time nonlinear systems whose dynamics’ uncertainty cannot be linearly parameterized. The method employs a Gaussian radial basis function network whose structure is derived from assumed smoothness of the nonlinearities, with Lyapunov‑based weight updates ensuring stability, and its performance is demonstrated in simulations. The algorithm is globally stable, driving tracking errors to a small neighborhood of zero under mild smoothness assumptions.

Abstract

A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture uses a network of Gaussian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibit by the nonlinear functions, the algorithm is proven to be globally stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with example systems.