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In this new study, we investigate the motion of a forced mass-spring-damper in a vertical position. First, the classical Lagrangian as well as the classical Euler–Lagrange equation of motion are constructed. Then the fractional Euler–Lagrange equation is derived by extending the classical Lagrangian in the fractional sense. In this extension, a new form of the fractional derivative is employed including a general function as its kernel. The derived fractional Euler–Lagrange equation is then converted into a system of linear algebraic equation by designing an efficient matrix approximation approach. The numerical findings are reported verifying the theoretical investigations. According to the results, some remarkable thinks are achieved; indeed, the numerical simulations show that different aspects of the system under study can be explored with regard to the flexibility found in selecting the kernel contrary to the traditional fractional models. [ABSTRACT FROM AUTHOR]

Steady-state periodic responses for a vibration system with distributed order derivatives are investigated, where the fractional derivative operator -∞Dt β is utilized. The response to complex harmonic excitation is derived and the amplitude–frequency and phase–frequency relations are obtained. For a periodic excitation, we decompose it into the Fourier series, and then make use of the principle of superposition and the results of harmonic excitations to obtain the response. Finally, we examine three numerical examples by using the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument. By means of the Lagrange multiplier in the calculus of variations and using the formula for fractional integration by parts, the Euler–Lagrange equations are derived in terms of a two-point fractional boundary value problem including an advance term as well as the delay argument. The derived equations are then reduced into a linear programming problem by using a Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations. The new scheme is also effective for the delay fractional optimal control problems influenced by the external persistent disturbances. Numerical simulations and comparative results verify that the proposed approach is efficient and easy to implement. [ABSTRACT FROM AUTHOR]

The behaviors of some vibrating dynamic systems cannot be modeled precisely by means of integer representation models. Fractional representation looks like it is more accurate to model such systems. In this study, the fractional Euler–Lagrange equations model is introduced to model a fractional damped oscillating system. In this model, the fractional inertia force and the fractional damping force are proportional to the fractional derivative of the displacement. The fractional derivative orders in both forces are considered to be variable fractional orders. A numerical approximation technique is utilized to obtain the system responses. The discretization of the Coimbra fractional derivative and the finite difference technique are used to accomplish this approximation. The response of the system is verified by a comparison to a classical integer representation and is obtained based on different values of system parameters. [ABSTRACT FROM AUTHOR]

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 improvement on the control effort and tracking performance. [ABSTRACT FROM AUTHOR]

This paper presents a novel global sliding mode control technique for the stabilization of a class of uncertain and nonlinear dynamic systems with perturbation. Using the Lyapunov stability theory and linear matrix inequality, some sufficient conditions are deduced to guarantee the asymptotic stabilization of the system states and to modify the robustness of the system. To improve the robust performance, an innovative reaching control law is designed to guarantee a chattering-free finite time performance under the uncertainty and nonlinearities and is optimally tuned using a modified random search algorithm. Simulation results are provided to show the effectiveness of the suggested technique. [ABSTRACT FROM AUTHOR]

Chaos in discrete fractional maps has been reported very recently. In this study, the chaotic time series of fractional order is used in the scrambling technique and a novel image encryption scheme is designed. The fractional difference order and the chaotic coefficient play crucial roles in controlling chaotic behaviors. The encrypted results are analyzed, which shows that the encryption scheme is highly secure. [ABSTRACT FROM AUTHOR]

An introduction to the journal is presented in which the editor discusses various reports within the issue on topics including forest fires, drug resistance during therapy for HIV infections, and non-minimum phase system.

The main goal of this manuscript is to investigate a fractional optimal control problem subject to a dynamical system involving Hadamard fractional derivatives. Necessary conditions for the optimality of the considered problem are derived in terms of the corresponding Euler–Lagrange equations. An iterative method is also proposed to numerically solve the obtained equations from the necessary optimality conditions. Two illustrative examples are considered and simulated in order to show the applicability and efficiency of the proposed method. Numerical simulations show that the used method presents some satisfying results regarding the absolute error values. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop an efficient iterative approach for solving a class of time-delay optimal control problems with time-varying delay and external persistent disturbances. By using the internal model principle, the original time-delay model with disturbance is first converted into an augmented system without any disturbance. Then, we select a quadratic performance index for the augmented system to form an undisturbed time-delay optimal control problem. The necessary optimality conditions are then derived in terms of a two-point boundary value problem involving advance and delay arguments. Finally, a fast iterative algorithm is designed for the latter advance-delay boundary value problem. The convergence of the new iterative technique is also investigated. Numerical simulations verify that the proposed approach is efficient and provides satisfactory results. [ABSTRACT FROM AUTHOR]

Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann–Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased. [ABSTRACT FROM AUTHOR]

In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana–Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme. [ABSTRACT FROM AUTHOR]

Recently some semi-analytical methods have been introduced for solving a class of nonlinear optimal control problems such as the Adomian decomposition method, homotopy perturbation method and modified variational iteration method. In this manuscript we compare these methods for solving a type of nonlinear optimal control problem. We prove that these methods are equivalent, which means that they use the same iterative formula to obtain the approximate/analytical solution. [ABSTRACT FROM AUTHOR]

This study introduces a novel 3-D fractional chaotic system with two quadratic terms and no equilibrium point. Thorough dynamical analysis of the introduced system is done studying Lyapunov dynamics with respect to fractional order and parameter value, Kaplan–Yorke dimension, bifurcation analysis, phase portraits, existence, and uniqueness of solution, dissipative and symmetric character, etc. The novel system is anti-synchronized using the novel technique 'triple compound combination' considering uncertainties and disturbances on a parallel system by two methods—nonlinear and adaptive sliding mode control. A proposed application of achieved synchronization in secure communication is presented. A comparative study of obtained results with published literature is also presented. [ABSTRACT FROM AUTHOR]

In this paper, the fractional order of a new chaotic system was studied and the minimum effective dimension for which the system remains chaotic was calculated. We have presented the chaos synchronization of two identical and nonidentical fractional orders of the new system by using active control. Furthermore, the Laplace transform and the Niemann–Trouvaille fractional integral operator were used for synchronizing two system. [ABSTRACT FROM PUBLISHER]

The main objectives of this study are to introduce a new class of optimal control problems governed by a dynamical system of weakly singular variable-order fractional integral equations and to establish a computational method by utilizing the Chebyshev cardinal functions for their numerical solutions. In this way, a new operational matrix of variable-order fractional integration is generated for the Chebyshev cardinal functions. In the established method, first the control and state variables are approximated by the introduced basis functions. Then, the interpolation property of these basis functions together with their mentioned operational matrix is applied to derive an algebraic equation instead of the objective function and an algebraic system of equations instead of the dynamical system. Eventually, the constrained extrema technique is applied by adjoining the constraints generated from the dynamical system to the objective function using a set of Lagrange multipliers. The accuracy of the established approach is examined through several test problems. The obtained results confirm the high accuracy of the presented method. [ABSTRACT FROM AUTHOR]

The phenomenon of thermoelastic damping (TED) is a well-known mechanism of structural damping in which a vibrating thermoelastic structure obeys energy dissipation caused by the irreversible heat conduction in its volume. TED can be listed as common intrinsic losses and it cannot be controlled as easily as extrinsic losses thus this subject appears to be a very attractive research field. In this study TED of in-plane vibration of a functionally graded material (FGM) nano-plate has been studied based on the Eringen nonlocal theory. The effects of main parameters such as ambient temperature, length, and width of the nano-plate, the nonlocal parameter and the material gradient on the quality factor (Q) have been investigated. Also, the effect of different combinations of ceramic and metal in an FGM plate on increasing Q and subsequently reduction of the dissipated energy due to thermal effects has been illustrated. [ABSTRACT FROM AUTHOR]

The cruise control problem of high speed trains (HSTs) is revisited in this paper. Despite the ongoing trend of using Lyapunov-based approaches, the concept of passivity is used as the basis of cruise controller design. To begin with, the Euler–Lagrange modeling of longitudinal motion of HST is introduced. Consequently, passivity properties of the system is investigated and it is shown that the system presents a strictly passive input–output map output. This property is utilized to design a controller based on an energy-shaping method. Since the controller benefits from the passivity property of the train, it is structurally simple and computationally efficient while ensuring asymptotic velocity tracking. In addition, as revealed in our robust analysis, the controller is capable of dealing with bounded perturbations. That is to say, boundedness of velocity tracking errors is guaranteed for sufficiently large control feedback gains. The obtained theoretical results have been verified by numerical simulation. [ABSTRACT FROM AUTHOR]