Asymptotic Tracking for Uncertain Dynamic Systems via a Multilayer NN Feedforward and RISE Feedback Control Structure

Abstract

The use of a neural network (NN) as a feedforward control element to compensate for nonlinear system uncertainties has been investigated for over a decade. Typical NN-based controllers yield uniformly ultimately bounded (UUB) stability results due to residual functional reconstruction inaccuracies and an inability to compensate for some system disturbances. Several researchers have proposed discontinuous feedback controllers (e.g., variable structure or sliding mode controllers) to reject the residual errors and yield asymptotic results. The research in this paper describes how a recently developed continuous robust integral of the sign of the error (RISE) feedback term can be incorporated with a NN-based feedforward term to achieve semi-global asymptotic tracking. To achieve this result, the typical stability analysis for the RISE method is modified to enable the incorporation of the NN-based feedforward terms, and a projection algorithm is developed to guarantee bounded NN weight estimates.

A new Robust ‘Integral of Sign of Error’ feedback controller with adaptive compensation gain

“…where z (t) was defined in (13). From the proofs of Lemmas 1 and 2, it is clear that P 1 (t) and P 2 (t) are non-negative and thus V (y, t) is also nonnegative.…”

“…can be utilized to prove that z (t) → 0 as t → ∞, and from its definition in (13), it is clear that the tracking error and its time derivatives asymptotically converge to zero.…”

“…Specifically, the constant uncertainty compensation gain in RISE feedback formulations require the knowledge of the upper bounds of vectors (functions of the desired system trajectories) containing system uncertainties. To reduce the heavy control effort enforced to the system by this high gain, researchers used adaptive [7] and neural network (NN) based [13], [14] feedforward compensation techniques in conjunction with RISE feedback. Recently, in [15], Jagannathan et.…”

Optimal Design of a RISE Feedback Controller for a 3-DOF Robot Manipulator Using Particle Swarm Optimization

“…In [19], Patre et al utilized this method to develop a tracking controller in presence of additive disturbances and parametric uncertainties. The RISE method is a high gain feedback tool.…”

A self tuning RISE controller formulation

“…In cases where this information is not available simply applying extra high gains to compensate for the system uncertainties is not a preferred approach. Researchers applied adaptive [5] and neural network (NN) based [11], [12] feedforward compensation techniques in conjunction with RISE feedback in order to decrease the heavy control effort enforced to the system by this high gain.…”