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1
Content available Robust continuous third-order finite time sliding mode controllers for exoskeleton robot
Fellag Ratiba, Guiatni Mohamed, Hamerlain Mustapha, Achour Noura
Archive of Mechanical Engineering
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2021
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LXVIII, nr 4
395--414
EN
In this work, continuous third-order sliding mode controllers are presented to control a five degrees-of-freedom (5-DOF) exoskeleton robot. This latter is used in physiotherapy rehabilitation of upper extremities. The aspiration is to assist the movements of patients with severe motor limitations. The control objective is then to design adept controllers to follow desired trajectories smoothly and precisely. Accordingly, it is proposed, in this work, a class of homogeneous algorithms of sliding modes having finite-time convergence properties of the states. They provide continuous control signals and are robust regardless of non-modeled dynamics, uncertainties and external disturbances. A comparative study with a robust finite-time sliding mode controller proposed in literature is performed. Simulations are accomplished to investigate the efficacy of these algorithms and the obtained results are analyzed.
2
Content available remote Oscillation criteria for higher order differential equations with positive and negative coefficients
Shoukaku Yutaka
Fasciculi Mathematici
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2019
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nr 62
121--140
EN
A new sufficient conditions for the oscillation of all solutions of higher order neutral delay differential equations with positive and negative coefficients are given. Because, we did not find a paper which gave conditions to guarantee the existence of oscillatory solutions for those equations with positive and negative coefficients. The main distinguishing feature of results is oscillation theorems for all solutions of those homogeneous or nonhomogeneous neutral equations are derived. These oscillation criteria extend and improve the results given in the recent papers.
3
Oscillatory behavior of higher order nonlinear homogeneous neutral delay dynamic equations with positive and negative coefficients
Panigrahi S., Reddy P. R.
Journal of Applied Analysis
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2018
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Vol. 24, nr 2
139--154
EN
In this paper, we derive some sufficient conditions for the oscillatory and asymptotic behavior of solutions of the higher order nonlinear neutral delay dynamic equation with positive and negative coefficients. The results of this paper extend and generalize the results of [S. Panigrahi and P. Rami Reddy, Oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations, Dyn. Contin. Discrete Impuls. Syst. Ser. AMath. Anal. 20 (2013), 143-163] and [S. Panigrahi, J. R. Graef and P. Rami Reddy, Oscillation results for fourth order nonlinear neutral dynamic equations, Commun. Math. Anal. 15 (2013), 11-28]. Examples are included to illustrate the validation of the results.
4
Anti-periodic solutions for a higher order difference equation with p-Laplacian
Kong L., Parsley J., Rizzo K., Russell N.
Journal of Applied Analysis
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2017
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Vol. 23, nr 2
111--125
EN
A higher order difference equation is studied. The equation is defined onℤand contains a p-Laplacian and both advance and retardation. Some criteria are established for the existence of infinitely many anti-periodic solutions of the equation. Several consequences of the main theorems are also included. Two examples are provided to illustrate the applicability of the results.
5
Content available remote Oscillation of higher-order half-linear neutral differential equations
Tang S., Li T., Thandapani E.
Demonstratio Mathematica
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2013
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Vol. 46, nr 1
101--109
EN
In this paper, we establish some new oscillation criteria for the higher-order half-linear neutral differential equation (…). An example is given to illustrate the main results.
6
Content available remote Architecture of iterative solvers for hp-adaptive finite element codes
Płaszewski P., Banaś K., Paszyński M.
Computer Assisted Methods in Engineering and Science
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2013
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Vol. 20, no. 1
43--54
EN
We present a layered architecture for iterative solvers of linear equations, designed to allow for easy integration with existing hp-adaptive FEM codes. We discuss interfaces between a solver and an external FEM code and requirements for the FEM code that must be met in order to work with the solver. Our solution is suited to work effectively with stationary as well as time-dependent problems. In this article, we provide an overview of the layered solver's structure and modules of each layer. In subsequent articles, we will present specific implementations of particular layers.
7
Content available remote On integrated Volterra integrodifferential equation of higher order
Pachpatte B. G.
Fasciculi Mathematici
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2008
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Nr 39
47-61
EN
In this paper we study the existence and other properties of solutions of a certain iterated Volterra integrodifferential equation of higher order. The tools employed in the analysis are based on application of the Leray-Schauder alternative and a certain integral inequality which provides explicit bound on the unknown function.
8
Content available remote On higher order Volterra-Fredholm integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
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2007
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Nr 37
35-48
EN
In the present paper we study the existence, uniqueness and other properties of soltions of a certain higher order Volterra-Fredholm integrodifferential equation. The well known Banach fixed point theorem coupled with Bilecki type norm and the new integral inequality with explicit estimate are used to establish the results.
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