Adaptive neural network control for a nonlinear Euler‐Bernoulli beam in three‐dimensional space with unknown control direction

Abstract

SummaryIn this paper, an adaptive neural network control system is developed for a nonlinear three‐dimensional Euler‐Bernoulli beam with unknown control direction. The Euler‐Bernoulli beam is modeled as a combination of partial differential equations (PDEs) and ordinary differential equations (ODEs). Adaptive radial basis function–based neural network control laws are designed to determine approximation of disturbances. A projection mapping operator is adopted to realize bounded approximation of disturbances. A Nussbaum function is introduced to compensate for the unknown control direction. The goal of this study is to suppress the vibrations of the Euler‐Bernoulli beam in three‐dimensional space. In addition, unknown control direction problem and bounded disturbances are considered to guarantee that the signals of the system are uniformly bounded. Numerical simulations demonstrate the effectiveness of the proposed method.