Vol. 10, No. 4 (2026): Regular Issue

This paper explores the control of a class of non-holonomic system using two distinct techniques: adaptive backstepping and stability in finite time through terminal sliding mode control (TSMC), with a particular focus on the Brockett system. An adaptive backstepping-based controller is designed to achieve global uniform asymptotic stability without requiring the conversion of the system model into a chained form, simplifying the implementation. In parallel, TSMC is applied to Brockett's system to achieve finite-time stabilization, providing rapid convergence and robustness against system uncertainties and disturbances. The controllability Lie algebra of Brockett's system contains Lie brackets of depth one, facilitating the application of both methods. Numerical simulations demonstrate the effectiveness of adaptive backstepping for asymptotic stabilization and the capability of TSMC to ensure finite-time convergence. This work underscores the strengths of both techniques in addressing the control challenges of Brockett's system.

Photovoltaic (PV) structures are increasingly deployed in environments where they are exposed to dynamic loads, particularly wind-induced vibrations. These vibrations can negatively affect the mechanical stability, performance, and energy efficiency of the system. This paper presents a numerical study focused on the implementation of active vibration control (AVC) using piezoelectric materials integrated into PV structures as both sensors and actuators. A simplified lumped-parameter dynamic model is developed to simulate the structural response of PV panels subjected to variable wind loads. The control strategy is based on a Linear Quadratic Regulator (LQR), which is designed to minimize displacement and improve system stability in real time. MATLAB simulations are conducted to investigate the influence of several parameters, including structural stiffness, panel inclination angle, thickness, and aerodynamic load. The results show a significant reduction in vibration amplitudes when active control is applied, even in the presence of sinusoidal disturbances. This work provides a foundational framework for integrating smart materials and adaptive control algorithms into future PV panel designs, improving their durability and efficiency under fluctuating environmental conditions.

This paper investigates the microcontroller execution, random number generator (RNG), and chaos suppression via genetic algorithms (GAs) in the piecewise resistive capacitive inductive shunted Josephson junction (JJ) oscillator (PRCLSJJO). Limit cycle, period-2 oscillations, periodic bursting characteristics, and six different shapes of chaotic characteristics are revealed in the PRCLSJJO. These dynamical characteristics obtained during the numerical simulations are validated by the microcontroller execution of the PRCLSJJO. The randomness of the generated binary data is extensively tested using the National Institute of Standards and Technology (NIST) SP 800-22 test suite, confirming the suitability of PRCLSJJO-based Random Number Generator (RNG) for applications such as secure communication schemes and other chaos-based applications. Chaos suppression in PRCLSJJO through GAs is demonstrated by optimizing some parameters of PRCLSJJO via the GAs. The chaotic characteristics encountered in PRCLSJJO can be converged to the desired state.

In this paper, we investigate the initial value problem for a two-component Camassa-Holm system (symmetric Keyfitz-Kranzer type model). Under suitable growth conditions, we establish existence of at least one classical solution via fixed-point arguments in a Banach space, existence of at least two nonnegative classical solutions in the positive cone using expansive-contraction methods, and existence of at least three distinct nonnegative classical solutions via coincidence degree theory on annuli. An explicit example has been demonstrated to verify all hypotheses.

Fault detection can effectively reduce maintenance costs, unplanned downtime, manual inspection's errors, and safety hazards. of non-invasive mechanical fault identification This study explores machine learning techniques for automated fault classification using vibration data. A test rig was fabricated for this purpose. Various supervised learning algorithms, including Naïve Bayes, Logistic Regression, Deep Learning, Decision Trees, Random Forest, and Support Vector Machines (SVM), were evaluated for their classification accuracy. Additionally, Deep Learning Convolutional Neural Networks (CNNs) were applied to classify faults based on images of time-domain and frequency-domain vibration signals. Results indicate that frequency-domain images outperform time-domain images in fault identification, achieving an average accuracy of 50% compared to 23%. It was also demonstrated that the low accuracy achieved can be enhanced by increasing the size of dataset. This research demonstrates the potential of image-based AI-driven fault detection.

This paper presents a comprehensive review of recent developments in energy harvesting (EH) from quasi-periodic (QP) vibrations in nonlinear oscillatory systems, particularly those incorporating time-delay effects. Unlike traditional resonance-based harvesting strategies that often suffer from narrow bandwidth and stability issues, QP-based approaches offer enhanced robustness and a broader operational frequency range. The study focuses on various delayed nonlinear oscillators-including Van der Pol, Duffing, Van der Pol-Duffing, Duffing-Mathieu-Van der Pol, and galloping-type systems-each c oupled to piezoelectric transducers. These configurations explore both constant and modulated feedback delays in either the mechanical or electrical domains. The analysis synthesizes insights from analytical approximations, bifurcation analysis, and numerical simulations, highlighting how delay-induced dynamics and QP responses can be harnessed to improve harvesting efficiency. By strategically tuning the delay parameters, large-amplitude QP oscillations can be stabilized even away from resonance, circumventing common issues such as bistability and amplitude jumps. The findings underscore the potential of delay engineering as a viable route toward broadband and efficient energy harvesting in both macro and microscale systems.

In this paper, dynamics of a frictional oscillator on the displacement-related belt boundary is studied. To understand dynamics of such a frictional oscillator, analytical conditions of motion switching on the nonlinear boundary are developed. For each domain, the linear oscillator solutions are given. From such solutions and motion switching conditions, periodic motions of the frictional oscillator is obtained, and numerical results give illustrations of periodic motions with switchability conditions at the boundary. From such methodology, dynamics of nonlinear frictional oscillators is studied in sequel. The analytical framework developed in this paper can be applied for discontinuous dynamical systems with state-dependent boundaries, the analytical conditions for grazing, sliding, and passable motions can be developed.