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An ISS-modular approach for adaptive neural control of pure-feedback systems. (English) Zbl 1137.93367
Summary: Controlling non-affine non-linear systems is a challenging problem in control theory. In this paper, we consider adaptive neural control of a completely non-affine pure-feedback system using radial basis function neural networks. An ISS-modular approach is presented by combining adaptive neural design with the backstepping method, Input-to-State Stability (ISS) analysis and the small-gain theorem. The difficulty in controlling the non-affine pure-feedback system is overcome by achieving the so-called “ISS-modularity” of the controller-estimator. Specifically, a neural controller is designed to achieve ISS for the state error subsystem with respect to the neural weight estimation errors, and a neural weight estimator is designed to achieve ISS for the weight estimation subsystem with respect to the system state errors. The stability of the entire closed-loop system is guaranteed by the small-gain theorem. The ISS-modular approach provides an effective way for controlling non-affine non-linear systems. Simulation studies are included to demonstrate the effectiveness of the proposed approach.

##### MSC:
 93C40 Adaptive control/observation systems 93C10 Nonlinear systems in control theory 93B52 Feedback control 93D25 Input-output approaches in control theory 92B20 Neural networks for/in biological studies, artificial life and related topics
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