Learning from neural control of nonlinear systems in normal form
Date
2009
Authors
Liu, Tengfei
Wang, Cong
Hill, David
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
A deterministic learning theory was recently proposed which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of simple nonlinear systems. In this paper, we investigate deterministic learning from adaptive neural control (ANC) of a class of nonlinear systems in normal form with unknown affine terms. The existence of the unknown affine terms makes it difficult to achieve learning by using previous methods. To overcome the difficulties, firstly, an extension of a recent result is presented on stability analysis of linear time-varying (LTV) systems. Then, with a state transformation, the closed-loop control system is transformed into a LTV form for which exponential stability can be guaranteed when a partial persistent excitation (PE) condition is satisfied. Accurate approximation of the closed-loop control system dynamics is achieved in a local region along a recurrent orbit of closed-loop signals. Consequently, learning of control system dynamics (i.e. closed-loop identification) from adaptive neural control of nonlinear systems with unknown affine terms is implemented.
Description
Keywords
Keywords: Adaptive neural control; Closed-loop identification; Deterministic learning; Normal form; Persistent excitation (PE) condition; Adaptive control systems; Control system analysis; Control system stability; Education; Identification (control systems); Nonli Adaptive neural control; Closed-loop identification; Deterministic learning; Nonlinear systems; Normal form; Persistent excitation (PE) condition
Citation
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Source
Systems and Control Letters
Type
Journal article