Robust linearization scheme by structural state feedback for a quadrotor

In this work a feedback linearization technique is proposed, to carry it out to linearize the dynamic model of the quadrotor, a change of variable is introduced that maps the nonlinearities of the system into a nonlinear uncertainty signal contained in the domain of the action of control and is applied to the dynamic model of the quadrotor. To estimate the nonlinear uncertainty signal, the Beard-Jones filter is used, which is based on standard state observers. To verify the effectiveness of the proposed control scheme, experiments are carried out outdoors to follow a circular trajectory in the (x,y) plane. This presented control scheme is suitable for unmanned aerial vehicles where it is important to reject not only non-linearities but also to seek the simplicity and effectiveness of the control scheme for its implementation.

Solving Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique

In this paper, using a suitable change of variable and applying the Adomian decomposition method to the generalized nonlinear Schr¨odinger equation, we obtain the analytical solution, taking into account the parameters such as the self-steepening factor, the second-order dispersive parameter, the third-order dispersive parameter and the nonlinear Kerr effect coefficient, for pulses that contain just a few optical cycle. The analytical solutions are plotted. Under influence of these effects, pulse did not maintain its initial shape.

Study of Fractional Analytic Functions and Local Fractional Calculus

In this present paper, the role of fractional analytic function in local fractional calculus is studied. Some important properties and theorems in local fractional calculus are discussed, such as product rule, quotient rule, chain rule, fundamental theorem of local fractional calculus, change of variable, integration by parts and so on. In addition, we propose several examples and formulas of local fractional calculus.

A Remark on the Change of Variable Theorem for the Riemann Integral

In 1961, Kestelman first proved the change in the variable theorem for the Riemann integral in its modern form. In 1970, Preiss and Uher supplemented his result with the inverse statement. Later, in a number of papers (Sarkhel, Výborný, Puoso, Tandra, and Torchinsky), the alternative proofs of these theorems were given within the same formulations. In this note, we show that one of the restrictions (namely, the boundedness of the function f on its entire domain) can be omitted while the change of variable formula still holds.

Robust classification with feature selection using an application of the Douglas-Rachford splitting algorithm

This paper deals with supervised classification and feature selection with application in the context of high dimensional features. A classical approach leads to an optimization problem minimizing the within sum of squares in the clusters (I2 norm) with an I1 penalty in order to promote sparsity. It has been known for decades that I1 norm is more robust than I2 norm to outliers. In this paper, we deal with this issue using a new proximal splitting method for the minimization of a criterion using I2 norm both for the constraint and the loss function. Since the I1 criterion is only convex and not gradient Lipschitz, we advocate the use of a Douglas-Rachford minimization solution. We take advantage of the particular form of the cost and, using a change of variable, we provide a new efficient tailored primal Douglas-Rachford splitting algorithm which is very effective on high dimensional dataset. We also provide an efficient classifier in the projected space based on medoid modeling. Experiments on two biological datasets and a computer vision dataset show that our method significantly improves the results compared to those obtained using a quadratic loss function.

Approach to the Formulation of the Variable Change Theorem

This research proposes a didactic strategy to enrich the assimilation processes of the change of variable theorem in solving the definite integral. The theoretical foundations that support it are based on the contributions of social constructivism, problem solving, and treatment of theorems. The practical validation of the strategy is carried out with students of the Higher Technical Level in Applied Mathematics at the Autonomous University of Guerrero.

Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays

In the present work, we mainly focus on a new established fractional-order predator-prey system concerning both types of time delays. Exploiting an advisable change of variable, we set up an isovalent fractional-order predator-prey model concerning a single delay. Taking advantage of the stability criterion and bifurcation theory of fractional-order dynamical system and regarding time delay as bifurcation parameter, we establish a new delay-independent stability and bifurcation criterion for the involved fractional-order predator-prey system. The numerical simulation figures and bifurcation plots successfully support the correctness of the established key conclusions.

Positive solutions for a class of generalized quasilinear Schrödinger equation involving concave and convex nonlinearities in Orilicz space

In this paper, we study the following generalized quasilinear Schrödinger equation − div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = λ f ( x , u ) + h ( x , u ) , x ∈ R N , where λ > 0 , N ≥ 3 , g ∈ C 1 ( R , R + ) . By using a change of variable, we obtain the existence of positive solutions for this problem with concave and convex nonlinearities via the Mountain Pass Theorem. Our results generalize some existing results.

Existence and asymptotic behavior of standing wave solutions for a class of generalized quasilinear Schrödinger equations with critical Sobolev exponents

In this paper, we study the following generalized quasilinear Schrödinger equation − div ( ε 2 g 2 ( u ) ∇ u ) + ε 2 g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = K ( x ) | u | p − 2 u + | u | 22 ∗ − 2 u , x ∈ R N , where N ⩾ 3, ε > 0, 4 < p < 22 ∗ , g ∈ C 1 ( R , R + ), V ∈ C ( R N ) ∩ L ∞ ( R N ) has a positive global minimum, and K ∈ C ( R N ) ∩ L ∞ ( R N ) has a positive global maximum. By using a change of variable, we obtain the existence and concentration behavior of ground state solutions for this problem with critical growth, and establish a phenomenon of exponential decay. Moreover, by Ljusternik–Schnirelmann theory, we also prove the existence of multiple solutions.