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Robust neural network control of robotic manipulators via switching strategy

Lei Yu;  Shumin Fei;  Jun Huang;  Yongmin Li;  Gang Yang;  Lining Sun — 2015

Kybernetika

In this paper, a robust neural network control scheme for the switching dynamical model of the robotic manipulators has been addressed. Radial basis function (RBF) neural networks are employed to approximate unknown functions of robotic manipulators and a compensation controller is designed to enhance system robustness. The weight update law of the robotic manipulator is based on switched multiple Lyapunov function method and the periodically switching law which is suitable for practical implementation...

On Kirchhoff type problems involving critical and singular nonlinearities

Chun-Yu Lei;  Chang-Mu Chu;  Hong-Min Suo;  Chun-Lei Tang — 2015

Annales Polonici Mathematici

In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ - ( a + b ∫ Ω | ∇ u | ² d x ) Δ u = u ⁵ + λ u q - 1 / | x | β in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.

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