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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:
93C40Adaptive control systems
93C10Nonlinear control systems
93B52Feedback control
93D25Input-output approaches to stability of control systems
92B20General theory of neural networks (mathematical biology)
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