Feedback error learning and nonlinear adaptive control

Abstract

In this paper, we present our theoretical investigations of the technique of feedback error learning (FEL) from the viewpoint of adaptive control. We first discuss the relationship between FEL and nonlinear adaptive control with adaptive feedback linearization, and show that FEL can be interpreted as a form of nonlinear adaptive control. Second, we present a Lyapunov analysis suggesting that the condition of strictly positive realness (SPR) associated with the tracking error dynamics is a sufficient condition for asymptotic stability of the closed-loop dynamics. Specifically, for a class of second order SISO systems, we show that this condition reduces to K 2 D . K P ; where K P and K D are positive position and velocity feedback gains, respectively. Moreover, we provide a 'passivity'-based stability analysis which suggests that SPR of the tracking error dynamics is a necessary and sufficient condition for asymptotic hyperstability. Thus, the condition K 2 D . K P mentioned above is not only a sufficient but also necessary condition to guarantee asymptotic hyperstability of FEL, i.e. the tracking error is bounded and asymptotically converges to zero. As a further point, we explore the adaptive control and FEL framework for feedforward control formulations, and derive an additional sufficient condition for asymptotic stability in the sense of Lyapunov. Finally, we present numerical simulations to illustrate the stability properties of FEL obtained from our mathematical analysis. q

Neural Network Based Modeling and Control for a Batch Heating/Cooling Evaporative Crystallization Process

“…The input and output data sets are generated from closed-loop control that is feedback controller (PID) to train the neural network [30][31][32][33]. In this section, the generated data for network training, which are the same as the forward model, consist of nominal and plant uncertainty cases ( -30% of U, +30% of Hcrys, -30% of Hevap, +30% of kg and +30% of kp).…”

Neurobiologically Inspired Distributed and Hierarchical System for Control and Learning

“…The convergence property of the FEL scheme was shown ( Gomi &Kawato 1993; Nakanishi & Schaal 2004). The FEL model has been developed in detail as a specific neural circuit model for three different regions of the cerebellum and the learning of the corresponding representative movements: 1) the flocculus and adaptive modification of the vestibuloocular reflex and optokinetic eye movement responses, 2) the vermis and adaptive posture control, and 3) the intermediate zones of the hemisphere and adaptive control of locomotion.…”

Real-Time Inverse Dynamics Learning for Musculoskeletal Robots based on Echo State Gaussian Process Regression

“…In these studies, feedforward neural networks were used to model the complex inverse dynamics of the manipulator, and feedback error learning [11,13] was employed to train the networks. However, as the structure of PAM-driven robots gets more complex, expressing its dynamics in the form of a static mapping is becoming difficult.…”