In this paper, a cybersecurity problem where the security team faces the challenge of preventing the hacker from breaching the multiple security layers is studied. The cybersecurity challenge mirrors the Chakravyuh, an ancient battlefield formation described in the Indian epic Mahabharata. The multi-layered complex structure of Chakravyuh, designed to trap the enemy, serves as an analogy for modelling the cybersecurity model of the digital economy. A hybrid model that integrates chaos theory and fuzzy logic is developed to enhance the defense mechanism in digitalization process. It is shown that the chaos theory approach can tackle the non-linear dynamics and unpredictable behavior of the hacker. On the other hand, fuzzy logic provides a more structured and adaptive defense mechanism. Monte Carlo simulations are used to analyze hacker’s breaching probability across security layers. Further, the Binary search algorithm is applied to optimize security layers dynamically while maintaining computational efficiency. This study integrates ancient wisdom with modern computational techniques to effectively mitigate cybersecurity threats.

In response to the lack of adaptability to individual differences in driving style for autonomous vehicles, an integrated planning and control method for autonomous driving that considers user’s steering style is proposed. Based on the artificial potential field theory, a vehicle motion path evaluation model is constructed, and the optimization goal is set as a comprehensive performance index of safety, comfort, and accuracy. The mathematical model of the integrated planning and control system for autonomous driving is established. Using natural driving data from user, a least squares method is employed to generate personalized steering style curves. Adecoding method based on steering style factors is proposed, followed using genetic algorithms to solve the optimization problem of integrated planning and control, obtaining the optimal steering control quantity that conforms to the user’s driving style and implementing personalized vehicle automatic steering control. Simulation experiments have verified the feasibility of the integrated planning and control strategy considering user’s steering style in typical driving scenarios, completing the identification and adaptation of user personalized steering style, and achieving the resolution of conflicts between autonomous driving and user’s driving style.

This paper investigates a class of multi-objective variational control problems, named (VCP), characterized by vector-valued integral objective/cost functional and differentiable inequality constraints. More precisely, we formulate the problem in a general framework and, in order to analyze optimality criteria, we associate scalar subproblems with the multi-objective setting and establish conditions under which efficient solutions of the original vector problem correspond to optimal solutions of these scalarized problems. We derive the necessary optimality conditions in the form of Euler–Lagrange-type equations, involving multipliers and piecewise smooth functions as variables. Furthermore, we introduce the new notion of (ϵ0, ϵ1) − (c0, c1) − type − I pair of functionals, adapted to the variational control setting. The introduced generalized convexity concepts are very important in characterizing efficient solutions and in deriving enhanced optimality conditions. These results enrich the theoretical framework of multi-objective variational control and provide a solid basis for future research and applications in mathematical optimization and control theory.

In this paper, the Linear Matrix Inequality (LMI) method is used to solve the problem of making observer-based control solutions for a class of uncertain linear systems. The study yields both control and observer gains derived from feasible LMI solutions. To illustrate the effectiveness of our approach, we present a practical example, showcasing the practicality and applicability of the proposed solutions.

In this work, we give sufficient conditions to get the existence of mild solutions for two classes of first-order semilinear functional and neutral functional perturbed evolution equations with infinite state-dependent delay when the conditions are nonlocal using Avramescu nonlinear alternative for the sum of compact operators and contraction maps in Fréchet spaces, combined with semigroup theory.

Transportation problems are a crucial area in logistics and operations research that focuses on effectively transporting products and resources from origin to destination. The complex nature of real-world situations requires the utilization of advanced mathematical models and optimization approaches to formulate effective solutions. Quantifying the accurate supply, demand, and transportation costs of transportation problems is highly challenging due to the market’s unpredictable economic and environmental conditions. Several methodologies have been proposed to address the issue of transportation problems with uncertain parameters, utilizing fuzzy theory and its derivatives. Complex Pythagorean fuzzy numbers (CPyFNs) are highly suitable and effective for representing uncertain and ambiguous information in real-world scenarios. This article introduces an innovative analysis of transportation problems in the complex Pythagorean fuzzy information framework. Initially,we establish an improved score function value to evaluate the ordering of CPyFNs more precisely and propose several ranking rules. The following section of the study presents mathematical formulations and optimization models for transportation problems, where the parameters are expressed as CPyFNs. The solution approach is formulated using Vogel’s approximation method (VAM) and modified distribution method (MODI) to solve transportation problems in a complex Pythagorean fuzzy setting. An illustrative numerical example is provided to showcase the practicality and effectiveness of the proposed method in real-life scenarios. The significance of the research and the extent of future investigation are also emphasized.

In the paper, two algorithms that allow identification of a parametric models of random time-series from binary-valued observations of their realizations, as well as from quantized measurements of their values, are proposed. The proposed algorithms are based on the idea of time-series decomposition either on a direct power spectral density or autocorrelation function approximation. They use the concepts of randomized search algorithms to recover the corresponding parametric models from calculated estimates of power spectral density or autocorrelation function. The considerations presented in the paper are illustrated with simulated identification examples in which linear and nonlinear block-oriented dynamic models of timeseries are identified from the binary-valued observations and quantized measurements.

This article investigates the impact of a high-voltage direct-current (HVDC) link and a wind turbine system (WTS) on the dynamics of a three-area thermal automatic generation control (AGC) system. A novel controller, the cascade of proportional-integral (PI) and tiltintegralderivative (TID) with filter coefficient (N) (PI-TIDN) controller is projected. The WTS units are subjected to various wind velocity scenarios, including fixed and random wind velocities. The controller parameters are concurrently enhanced using the hybrid crowsearch algorithm (HCSA). The system dynamics corresponding to the PI-TIDN controller are superior to those of PIDN and TIDN controllers. Additionally, studies with different wind velocities demonstrate that responses with fixed wind velocities are better than those with random wind velocities. Moreover, integrating WTS units with the thermal system improves dynamics compared to the thermal system alone. It is also apparent that the parallel AC-HVDC system enhances dynamics. Furthermore, sensitivity analysis exposes that the PI-TIDN controller values at nominal settings are vigorous and do not require retuning.

The Floquet-Lyapunov transformation is extended to fractional discrete-time linear systems with periodic parameters. A procedure for computation of the transformation is proposed and illustrated by a numerical example.

In the paper a new, fractional order, discrete transfer function model of an elementary inertial plant is proposed. The model uses Atangana-Baleanu and discrete Fractional Order Backward Difference operators to describe of the fractional derivative. Such a transfer models have not be presented yet. The analytical formula of the step response for time-continuous transfer function is given. The similarity of the proposed model to “classic” one using Caputo operator is also considered. The stability and the convergence of the discrete transfer function are analyzed. Theoretical results are expanded by simulations. The proposed discrete, approximated model is accurate and its numerical complexity is low. It can be useful in modeling of different physical phenomena, for example thermal processes.