In this paper, we discuss the question whether a physical “simplification” of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these simplifications often lead to worse mathematical properties of the solution to the model. This may affect the existence and uniqueness of...

We propose an original approach to solve the coupled problem of alternative magnetic field penetration inside a toroidal soft ferromagnetic sample and frequency dependent magnetic hysteresis. Local repartition of ferromagnetic losses depends on the instantaneous material properties and on the frequency of the excitation field waveform. A correct solution to the model, with...

The goal of the present work is to achieve nonlinear semi-global output feedback stabilization of variable speed grid connected direct drive wind turbine generator DDWTG systems under wind energy conversion systems to provide the electricity demand for electrical networks. The study will address the sensorless control of variable speed wind energy generation systems, namely...

Mathematical models offer crucial insights into the transmission dynamics and control of infectious diseases. These models have also been applied to investigate a variety of ‘contagious’ social phenomena like crime, opinions, addiction and fanaticism. We review the use and adaptation of models from epidemiology (compartmental models) to investigate the transmission dynamics of...

In the paper the explicit conditions for stability of linear fractional order h-difference systems with the Grünwald–Letnikov-type operator are presented. The state variables of the considered systems are taken from the plane. As the tool the \({\mathcal {Z}}\)-transform, which can be considered as an effective method for the stability analysis of linear systems, is used. The...

In this paper, the trapezoidal rule for the Grünwald-Letnikov operator is derived. It is a trapezoidal rule in the sense that the formula yields the exact Grünwald-Letnikov derivative/integral of a piecewise linear function. Firstly, the formula for evenly spaced points is derived, and is used as a basis to derive the equivalent formula for arbitrary abscissae. Further, an...

In this paper, a new alternative method for the determination of the set of all minimal positive and non-positive realisations of the one-dimensional fractional continuous-time linear systems based on the one-dimensional digraphs theory has been presented. In addition, all realisations in the set are minimal. For the proposed method, an algorithm was also constructed. The...

In this paper a simple method of the fractional-order linear digital filter response calculation is proposed. The fractional-order linear digital filter description is based on the fractional-order linear time-invariant difference equation and related fractional-order discrete transfer function.

On the basis of the documentation, the finite element beam model of the Shukhov’s tower has been constructed. In 1970–1971, after 50 years of exploitation, the study of the Shukhov’s tower was conducted by the specialists. This study has revealed serious defects of the individual elements. It was found that the rolled profiles reaches 10 % of the cross section due to corrosion...

Application of the MEBDFV code in multibody dynamics is discussed. The solver is based on the modified extended backward differentiation formulae of Cash. It is especially suited for the solution of differential-algebraic equations with time- and state-dependent mass matrix. Such a case can occur when motion of a multibody open-chain system is described within the classical...

In this work the problem of motion modeling and work cycle optimization of manipulator with revolute joints has been considered. The motion equations of the manipulator elements under any spatial work cycle conditions have been formulated. The formulation has been completed by using the classic vector mechanics and Lagrange equations of second kind. The equations of motion of the...

Vibrations of a nonlinear self- and parametrically excited MEMS device driven by external excitation and time delay inputs are analysed in the paper. The model of MEMS resonator includes a nonlinear van der Pol function producing self-excitation, a periodically varied coefficient which represents Mathieu type of parametric excitation and furthermore, periodic force acting on the...

This paper presents an indirect adaptive neural network sliding mode Control (IANSMC) technique and a neural network sliding mode control (NNSMC) for underactuated robot manipulators. The adaptive neural network (NN) based on radial basis functions (RBF) is used to estimate the equivalent control and to compensate model uncertainties. In IANSMC, the adaptive learning algorithms...

This paper investigates the feasibility and fundamental gait properties of active and passive limit-cycle walkers that walk on slippery road surface. First, we introduce the model of an underactuated spoked walker with a torso and mathematically analyze the collision model on the assumption of sliding contact with the ground to identify the condition for achieving instantaneous...

In this paper, we study a class of singular stochastic optimal control problems for systems described by mean-field forward-backward stochastic differential equations, in which the coefficient depend not only on the state process but also its marginal law of the state process through its expected value. Moreover, the cost functional is also of mean-field type. The control...

In this paper, a quantitative measure of partial observability is defined for PDEs. The quantity is proved to be consistent if the PDE is approximated using well-posed approximation schemes. A first order approximation of an unobservability index using an empirical Gramian is introduced. Several examples are presented to illustrate the concept of partial observability. The theory...

The aim of this article is control of a set of 3-wheel robots with non-holonomic dynamics for hunting and covering around moving target. Robots have mass and inertia, and the wheel mass have been considered in the dynamic model of robots. The output of the controller is wheel’s torque and steering torque of the front wheel. The saturation and filtering effects of the actuators...

In this paper, a systematic design procedure for generalized projective synchronization between two identical chaotic satellites systems based on feedback control theory is proposed. This method is developed based on suitable feedback control, combined with the Lyapunov stability theory and linear matrix inequality formulation as a solution of the optimal problem. Two necessary...

The paper presents selected issues of position-force control of electro-hydraulic servo system using adaptive methods. This kind of measure extends the capabilities of control system which uses only position measurements. Indirect adaptive control has allowed for the monitoring and updating the dynamic phenomena occurring in the drive.