In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyze the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, whic...

We propose a block-iterative parallel decomposition method to solve quadratic signal recovery problems under convex constraints. The idea of the method is to disintegrate the original multi-constraint problem into a sequence of simple quadratic minimizations over the intersection of two half-spaces constructed by linearizing blocks of constraints. The implementation of the algorithm is quite ex...

This paper reports on a new algorithm for the Generalized Quadratic Assignment problem (GQAP). The GQAP describes a broad class of quadratic integer programming problems, wherein M pairwise related entities are assigned to N destinations constrained by the destinations’ ability to accommodate them. This new algorithm is based on a Reformulation Linearization Technique (RLT) dual ascent procedur...

In this paper, we study time discretizations of fully nonlinear parabolic differential equations. Our analysis uses the fact that the linearization along the exact solution is a uniformly sectorial operator. We derive smooth and nonsmooth-data error estimates for the backward Euler method, and we prove convergence for strongly A(θ)stable Runge–Kutta methods. For the latter, the order of converg...

This article addresses the design of therapeutic procedures for cancer using a control based on the Gompertz model, that describes the nonlinear dynamics of tumor growth. The aim is to reduce the tumor size according to a decreasing target reference. The approach presented on this work uses a control Lyapunov function and yields an adaptive PI strategy that results from the exact linearization....

This note investigates the problem of plasma glucose regulation by means of subcutaneous insulin administration. A discrete delay differential equation model of the glucoseinsulin regulatory system has been considered, which properly takes into account also the pancreatic insulin release, in such a way to allow insulin therapies for both Type I and Type II diabetes (in this latter case the endo...

Quantum mechanics abounds in models with Hamiltonian operators which are energy-dependent. A linearization of the underlying Schrödinger equation with H = H(E) is proposed here via an introduction of a doublet of separate energyindependent representatives K and L of the respective right and left action of H(E). Both these new operators are non-Hermitian so that our formalism admits a natural ex...

In this paper some adaptive nonlinear multivariable techniques used in the control of robotic manipulators are presented. The nonlinear control law and state feedback are used in achieving a linear inputoutput behavior for the controlled system. For the design of the adaptive nonlinear control, the exact feedback input-output linearization and the method of gradient are used. The nonlinear cont...

The paper presents a new control method which achieves autonomous obstacle avoidance for manipulators with rate constraints. More precisely, in order to achieve the autonomous obstacle avoidance, we exploit the freedom of the coordinate transformation for exact linearization of nonlinear systems. At the same time, we cope with the rate constraints by adopting the statedependent time scale trans...

We consider the maximum feasible subsystem problem in which, given an infeasible system of linear inequalities, one wishes to determine a largest feasible subsystem. The focus is on the version with bounded variables that naturally arises in several fields of application. To tackle this NP-hard problem, we propose a simple but efficient two-phase relaxation-based heuristic. First a feasible sub...