The paper deals with the development of scientific backgrounds for increasing order of chaotic system and improving its cryptic properties. These backgrounds are based on transforming chaotic systems’ dynamics into multidimensional form by replacing one-dimensional state space variables with multidimensional state vectors. Such transformation can be performed in an easy way for the class of 1-st order nonlinear time-delayed dynamical objects by simple changing state variables. Complex and hypercomplex numbers are used to define both object’s state variables and its parameters. If only state variables are defined with hypercomplex numbers, one can find a chaotic system with several parallel channels without any interrelations between channel. Otherwise, if the object’s parameters are defined with multidimensional vectors, a parallel chaotic system with interrelations between channels can be defined.Since the proposed chaotic generator is implemented on the microcontroller, the transformation of the considered multidimensional chaotic system into discrete form is performed by using backward difference approximation of continuous time derivative operator. Discrete-time model of the multichannel chaotic system makes it possible to define structure, feedforward and feedback parameters of the considered system in an easy way as well as can be implemented on modern microcontrollers. As an example, we consider the Mackey-Glass chaotic system and extend it by using complex numbers. Such an approach allows us to design and implement two channel chaotic system. Since complex numbers are used. one can interpret chaotic oscillations in each channel as multidimensional chaotic oscillations, which are given by their projections or by amplitude and phase.

The paper deals with the developing of scientific backgrounds to design the control system for time-variant linear dynamical objects. These backgrounds are based on using the interval methods to transform time-variant models into interval time-invariant form. One can use control theory methods to perform the transformation of the designed model into the operator form. The proposed method allows us to describe a time-variant dynamical object by the interval differential equations with time-invariant factors. It is possible to define interval transfer functions for designed in such way models and one can use these transfer functions to define minimal and maximal controller's transfer function, which make it possible to transform control object into the desired form by solving an inverse dynamic problem and compensating object inner dynamic. We show various control methods can be used to control transformed object. We illustrate the usage of our methods by considering the example of controller design for UAV speed control.

Secured data transmission is one of the main branches of modern chaotic systems' usages. The paper deals with the study and usage of the Chua circuit model with a voltage source in each branch. Analysis of this model allows everybody to define preferable places for a set-up voltage source in the Chua circuit. Mentioned places make it possible to reduce Chua model and to simplify controller design which synchronizes two Chua circuits by using master-slave control technique. The high quality of this synchronization is granted by using sliding mode control algorithms. Usage of these algorithms allows us to compensate nonlinearity of considered circuit and changing of its parameters. We use the node-voltage method for developing the Chua circuit model with several voltage sources. Then we analyze the developed model and find that it is the best choice to use voltage sources which are connected in a serial way with capacitors. At third, we develop ta Chua circuit's interval model and use it to compensate nonlinearity of Chua diode. Then we write down full and reduced state space equations for the Chua circuit. At fifth, we use reduced interval equations to design a controller which performs synchronization of two Chua circuit.

This paper investigates, for the first time, the synthesis of a controller that incorporates a fractional-order integral component to achieve a closed-loop astaticism order greater than one. To enhance both static and dynamic accuracy, the controller integrates direct-signal-propagation neural networks within each control channel. The controlled plant is the BLDCM speed loop, which is modeled using a fractional-order differential equation. The study compares the performance of four controller types: a classical PID regulator tuned close to the optimal modulus criterion (IntPID); a fractional PI–PI^μD controller (FrPID) that achieves an astaticism order of at least 1.8; and two hybrid neuro-controllers, NN–IntPID and NN–FrPID. While the FrPID controller reduces the root-mean-square error by nearly a factor of five compared with IntPID, the best results are delivered by NN–FrPID. Specifically, it decreases overshoot eight-fold during a reference step (from 2.98% to 0.35%), lowers the root-mean-square error during linear reference tracking by a factor of eleven, and reduces the relative speed error by more than thirty-five times. When combined with a fast learning algorithm executed at each control-cycle iteration, the controller enables the closed loop to adapt not only to variations in gain coefficients, but also to changes in the fractional-aperiodic order of the plant. These results demonstrate that neural fractional-integral controllers offer strong potential for improving accuracy and robustness in BLDC motor drives and are applicable to a wide range of electromechanical systems.