Fractional Differential Equations

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Feel lonely? What about reading books? Book is one of the greatest friends to accompany while in your lonely time. When you have no friends and activities somewhere and sometimes, reading book can be a great choice. This is not only for spending the time, it will increase the knowledge. Of course the b=benefits to take will relate to what kind of book that you are reading. And now, we will concern you to try reading modelling and control of robot manipulators as one of the reading material to finish quickly.

Modelling and Control of Robot Manipulators

Adaptive control methods are developed for stability and tracking control of flight systems in the presence of parametric uncertainties. This paper offers a design technique of adaptive sliding mode control (ASMC) for finite-time stabilization of unmanned aerial vehicle (UAV) systems with parametric uncertainties. Applying the Lyapunov stability concept and finite-time convergence idea, the recommended control method guarantees that the states of the quad-rotor UAV are converged to the origin with a finite-time convergence rate. Furthermore, an adaptive-tuning scheme is advised to guesstimate the unknown parameters of the quad-rotor UAV at any moment. Finally, simulation results are presented to exhibit the helpfulness of the offered technique compared to the previous methods.

Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties.

In this paper, we discuss the conditions of existence and uniqueness of solutions to a certain class of ordinary differential equations involving Atangana–Baleanu fractional derivative. Benefiting from the Gronwall inequality in the frame of Riemann–Liouville fractional integral, we establish a Gronwall inequality in the frame of Atangana–Baleanu fractional integral. Then, we study the stability of such equations in the sense of Ulam.

On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative

This paper develops an adaptive super-twisting global nonlinear sliding mode control technique for n-link rigid robotic manipulators A novel control law is designed to guarantee elimination of the reaching phase and existence of the sliding mode around the surface right from the initial time Furthermore, the adaptive tuning law eliminates requirement of the knowledge about the upper bounds of external disturbances By using the proposed method, a robust controller is designed so that the tracking error of rigid manipulator is convergent to the global nonlinear sliding surface in a finite time, and strong robustness with respect to large uncertainties and disturbances is guaranteed Illustrative simulations on a two-link elbow robot manipulator and a three degree of freedom rigid manipulator are presented to show the robustness and effectiveness of the suggested design compared to other method Moreover, a simulation as well as experimental study of a rotary inverted pendulum system demonstrates the applicability of the proposed method

Design of an adaptive tracker for n-link rigid robotic manipulators based on super-twisting global nonlinear sliding mode control

Soliton solutions and conservation laws for lossy nonlinear transmission line equation

In this paper, an linear matrix inequalities (LMI)-based second-order fast terminal sliding mode control technique is investigated for the tracking problem of a class of non-linear uncertain systems with matched and mismatched uncertainties. Using the offered approach, a robust chattering-free control scheme is presented to prove the presence of the switching around the sliding surface in the finite time. Based on the Lyapunov stability theorem, the LMI conditions are presented to make the state errors into predictable bounds and the parameters of the controller are obtained in the form of LMI. The control structure is independent of the order of the model. Then, the proposed method is fairly simple and there is no difficulty in the use of this scheme. Simulations on the well-known Genesio's chaotic system and Chua's circuit system are employed to emphasize the success of the suggested scheme. The simulation results on the Genesio's system demonstrate that the offered technique leads to the superior impro...

Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems:

http://scientiairanica.sharif.edu/article_4123_4f7cf0ef6ee7d45c15a3a26acc031cd2.pdf

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

In this work, the coupled nonlinear Schrodinger’s equation (CNLSE) is studied with four forms of nonlinearity. The nonlinearities that are considered in this paper are the Kerr law, power law, parabolic law and dual-power law. Jacobi elliptic function solutions and also bright and dark optical soliton solutions are obtained for each law of the CNLSE. We will acquire constraint conditions for the existence of obtained solitons.

Fairouz Tchier

Papers

Design of an adaptive tracker for n-link rigid robotic manipulators based on super-twisting global nonlinear sliding mode control

Soliton solutions and conservation laws for lossy nonlinear transmission line equation

Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems:

Nonsingular fast terminal sliding-mode stabilizer for a class of uncertain nonlinear systems based on disturbance observer

Optical solitons of the coupled nonlinear Schrödinger's equation with spatiotemporal dispersion