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Summary In 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.

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The sliding mode control method is proposed for a class of underactuated systems with input constraint in this paper. The properties of hyperbolic tangent function are used to deal with input constraint. Furthermore, a radial basis function (RBF) neural network is adopted to achieve the approximation of the unknown function and the projection mapping operator is used to further guarantee the bounded approximation. The control law is designed by using the Lyapunov's direct method, and the stability is conducted by using Hurwitz stability analysis. In the simulation part, two examples are listed, including a simple underactuated system and an underactuated inverted pendulum system, which can all be transformed into the model style studied in this paper to illustrate the effectiveness of the proposed control law. At last, the conclusion is summarized.

SummaryThis paper proposes an adaptive boundary control scheme for the flexible three‐dimensional Euler‐Bernoulli beam with input signal quantization. Considering the coupling effect between the axial deformation and the transverse displacement, the dynamics of the flexible system are represented by partial differential equations and ordinary differential equations. Input signals in modern control systems are often quantized before being transmitted through communication channels in technology engineering. Logarithmic quantitative controllers are designed to suppress the vibration of the beam. It is proved that the proposed control scheme can be guaranteed in handling the vibration of the beam and input signal quantization simultaneously. Finally, numerical simulations illustrate the effectiveness of the results.

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