Gaussian networks for direct adaptive control

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.

Feedback error learning and nonlinear adaptive control

“…we know all the correct basis functions, D will be zero. If the structure of f is unknown, we can use a linearly parametrized function approximator such as locally linear models (Choi & Farrell;Nakanishi et al, 2002Nakanishi et al, , 2004Schaal & Atkeson, 1998) or RBF neural networks (Sanner & Slotine, 1992). In this paper, we assume a perfect approximation where D ¼ 0; the case where D -0 can be treated as in Nakanishi et al (2002Nakanishi et al ( , 2004 by introducing an adaptation deadzone for parameter update.…”

“…In order to facilitate a coherent development of our research results, in this section we review a general formulation of nonlinear adaptive control (Choi & Farrell, 2000;Sanner & Slotine, 1992;Slotine & Li, 1991) with the adaptive feedback controller as depicted in Fig. 2.…”

“…We first consider the formulation with the adaptive state feedback controller in Fig. 2 since it allows us to directly apply several theoretical results of the adaptive control framework (Choi & Farrell, 2000;Nakanishi et al, 2002Nakanishi et al, , 2004Sanner & Slotine, 1992). Subsequently, we investigate the formulation with the adaptive feedforward component in Fig.…”

“…In Section 3, we discuss the adaptive feedback formulation. In Section 3.1, we review the nonlinear adaptive control framework (Choi & Farrell, 2000;Sanner & Slotine, 1992;Slotine & Li, 1991). In Sections 3.2 and 3.3, we discuss the relationship between nonlinear adaptive control and FEL in the adaptive state feedback formulation.…”

Reinforcement learning control for coordinated manipulation of multi-robots

“…For the approximation of a continuous function h(Z) : R r → R, the following Radial Function Basis (RBF) Neural Networks (NN) are used [26]:…”