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Observer-based adaptive sliding mode fault-tolerant control for the underactuated space robot with joint actuator gain faults

Ronghua Lei, Li Chen (2021)

Kybernetika

An adaptive sliding mode fault-tolerant controller based on fault observer is proposed for the space robots with joint actuator gain faults. Firstly, the dynamic model of the underactuated space robot is deduced combining conservation law of linear momentum with Lagrange method. Then, the dynamic model of the manipulator joints is obtained by using the mathematical operation of the block matrices, hence the measurement of the angular acceleration of the base attitude can be omitted. Subsequently,...

On Lyapunov stability in hypoplasticity

Kovtunenko, Victor A., Krejčí, Pavel, Bauer, Erich, Siváková, Lenka, Zubkova, Anna V. (2017)

Proceedings of Equadiff 14

We investigate the Lyapunov stability implying asymptotic behavior of a nonlinear ODE system describing stress paths for a particular hypoplastic constitutive model of the Kolymbas type under proportional, arbitrarily large monotonic coaxial deformations. The attractive stress path is found analytically, and the asymptotic convergence to the attractor depending on the direction of proportional strain paths and material parameters of the model is proved rigorously with the help of a Lyapunov function....

On small solutions of second order differential equations with random coefficients

László Hatvani, László Stachó (1998)

Archivum Mathematicum

We consider the equation x ' ' + a 2 ( t ) x = 0 , a ( t ) : = a k if t k - 1 t < t k , for k = 1 , 2 , ... , where { a k } is a given increasing sequence of positive numbers, and { t k } is chosen at random so that { t k - t k - 1 } are totally independent random variables uniformly distributed on interval [ 0 , 1 ] . We determine the probability of the event that all solutions of the equation tend to zero as t .

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