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Abstract: This paper presents control studies of delayed dynamical systems with the help of the method of continuous time approximation (CTA). The CTA method proposes a continuous time approximation of the delayed portion of the response leading to a high and finite dimensional state space formulation of the time-delayed system. Various controls of the system such as LQR and output feedback controls are readily designed with the existing design tools. The properties of the method in frequency domain are also discussed. We have found that time-domain methods such as semi-discretization and CTA, and other numerical integration algorithms can produce highly accurate temporal responses and dominant poles of the system, while missing all the fast and high frequency poles, which explains why many numerical methods can be applied to study the stability of time-delayed systems, and may not be a good tool for control design. Optimal feedback controls for a linear oscillator, collocated and non-collocated feedback controls of an Euler beam, and an experimental demonstration are presented in the paper. [Copyright &y& Elsevier]

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to ill-conditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce the reconstruction of variational iteration method (RVIM) to solve multi-order fractional differential equations (M-FDEs), which include linear and nonlinear ones. We will easily obtain approximate analytical solutions of M-FDEs by means of the RVIM based on the properties of fractional calculus. Moreover, the convergence of proposed method will be shown. Our scheme has been constructed for the fully general set of M-FDEs without any special assumptions, and is easy to implement numerically. Therefore, our method is more practical and helpful for solving a broad class of M-FDEs. Numerical results are carried out to confirm the accuracy and efficiency of proposed method. Several numerical examples are presented in the format of table and graphs to make comparison with the results that previously obtained by some other well known methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove the convergence of a numerical algorithm that switches in some deterministic or random manner, the control parameter of a class of continuous-time nonlinear systems while the underlying initial value problem is numerically integrated. The numerically obtained attractor is a good approximation of the attractor obtained when the control parameter is replaced with the average of the switched values. In this way, a generalization of Parrondo’s paradox can be obtained. As an application, the Lorenz and Rabinovich–Fabrikant systems are used for illustration. [Copyright &y& Elsevier]

Abstract: In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures. [Copyright &y& Elsevier]

Abstract: The pseudo-randomness and complexity of binary sequences generated by chaotic systems are investigated in this paper. These chaotic binary sequences can have the same pseudo-randomness and complexity as the chaotic real sequences that are transformed into them by the use of Kohda’s quantification algorithm. The statistical test, correlation function, spectral analysis, Lempel–Ziv complexity and approximate entropy are regarded as quantitative measures to characterize the pseudo-randomness and complexity of these binary sequences. The experimental results show the finite binary sequences generated by the chaotic systems have good properties with the pseudo-randomness and complexity of sequences. However, the pseudo-randomness and complexity of sequence are not added with the increase of sequence length. On the contrary, they steadily decrease with the increase of sequence length in the criterion of approximate entropy and statistical test. The constraint of computational precision is a fundamental reason resulting in the problem. So only the shorter binary sequences generated by the chaotic systems are suitable for modern cryptography without other way of adding sequence complexity in the existing computer system. [Copyright &y& Elsevier]

Abstract: In this paper, a weighted algorithm based on the homotopy analysis method (HAM), for solving inverse heat conduction problems, is introduced . Using the HAM, it is possible to find the exact solution or an approximate solution of the problem in the form of a series. [Copyright &y& Elsevier]

Abstract: In this paper, reproducing kernel theorem is employed to solve anti-periodic solutions for Rayleigh-type equations. A simple algorithm is given to obtain the approximate solutions of the equations. By comparing the approximate solution with the exact analytical solution, we find that the simple algorithm is of good accuracy and it can be also applied to some ordinary or partial differential equations with initial-boundary value conditions and nonlocal boundary value conditions. [Copyright &y& Elsevier]

Abstract: In this paper, a new system of nonlinear (set-valued) variational inclusions involving -maximal relaxed monotone and relative -maximal monotone mappings in Hilbert spaces is introduced and its approximation solvability is examined. The notion of -maximal relaxed monotonicity generalizes the notion of general -maximal monotonicity, including -maximal monotonicity (also referred to as -monotonicity in literature). Using the general -resolvent operator method, approximation solvability of this system based on a generalized hybrid iterative algorithm is investigated. Furthermore, for the nonlinear variational inclusion system on hand, corresponding nonlinear Yosida regularization inclusion system and nonlinear Yosida approximations are introduced, and as a result, it turns out that the solution set for the nonlinear variational inclusion system coincides with that of the corresponding Yosida regularization inclusion system. Approximation solvability of the Yosida regularization inclusion system is based on an existence theorem and related Yosida approximations. The obtained results are general in nature. [Copyright &y& Elsevier]

Abstract: This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm. [Copyright &y& Elsevier]

Abstract: In this paper an algorithm based on Adomian’s decomposition method is developed to approximate the solution of the nonlinear fractional convection–diffusion equationThe fractional derivative is considered in the Caputo sense. The approximate solutions are calculated in the form of a convergent series with easily computable components. The analysis is accompanied by numerical examples and the obtained results are found to be in good agreement with the exact solutions known for some special cases. [Copyright &y& Elsevier]