Direct adaptive control algorithms: theory and applications
Direct adaptive control algorithms: theory and applications
Constructive incremental learning from only local information
Neural Computation
Control Theory of Nonlinear Mechanical Systems
Control Theory of Nonlinear Mechanical Systems
Nonlinear and Adaptive Control Design
Nonlinear and Adaptive Control Design
Nonlinear adaptive control using networks of piecewise linear approximators
IEEE Transactions on Neural Networks
SIMBICON: simple biped locomotion control
ACM SIGGRAPH 2007 papers
Letters: Adaptive biomimetic control of robot arm motions
Neurocomputing
Preventing bursting in approximate-adaptive control when using local basis functions
Fuzzy Sets and Systems
International Journal of Automation and Computing
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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 K2D Kp, where Kp, and KD) 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 K2D Kp 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.