Search Results (2,048)

This paper addresses the trajectory tracking control problem of Autonomous Underwater Vehicles (AUVs). A comprehensive mathematical model is first established based on Newtonian mechanics, incorporating both kinematic and dynamic equations. By reasonably neglecting the minor influence of roll motion, a five-degree-of-freedom (5-DOF) underactuated AUV model is derived. Considering the strong nonlinearities, high coupling, and time-varying hydrodynamic parameters typical of underwater environments, a fuzzy adaptive PID controller is proposed. This controller combines the adaptability of fuzzy logic with the structural simplicity and reliability of PID control, making it well-suited to the demanding requirements of AUV motion control. Extensive simulation experiments are conducted to evaluate the controller’s performance under various operating conditions. The results show that the fuzzy adaptive PID controller significantly outperforms conventional PID and standalone fuzzy logic controllers in terms of convergence speed and oscillation suppression. Furthermore, a theoretical stability analysis is provided to ensure that the proposed control system remains stable under time-varying fuzzy gain scheduling, confirming its effectiveness and potential for practical application in underwater vehicle control. Full article

Acid stimulation is a widely used technique for enhancing hydrocarbon recovery from carbonate reservoir formations. In this study, a mathematical model is developed to describe acidizing-induced pressure behavior in carbonate rocks, based on fluid dynamics and acid transport equations. The model is discretized using the finite volume method, resulting in a numerical framework suitable for simulating acidizing processes in carbonate reservoirs. Due to the model’s inherent characteristics—strong nonlinearity and the presence of high-dimensional sparse systems of equations—a sparse quasi-Newton method is proposed to efficiently solve the resulting system. Numerical experiments confirm the practicality and effectiveness of the proposed approach. Full article

The nonlinearity and non-convexity of the hydropower output function (HOF) make it very challenging to search for the optimal solution to the hydropower scheduling problem, which, however, can be more easily solved with consistency by mathematical programming if the HOF can be properly linearized with high accuracy. In this paper, a detailed review of different linear concaving approximation methods to model the HOF is presented, and a high-precision, all-rectangle linear concaving approximation method is proposed. It avoids the drawback of existing rectangular grid linear approximation methods which introduce a large number of integer variables and reduce solution efficiency by avoiding the accurate expression of fitting error at the corner points. It is mathematically proved that the method based on this rectangular subdivision can converge to any concave function with arbitrary precision as the grid resolution increases. The approximated results of the output functions of the four cascaded hydropower plants in the Lancang River show that both the proposed method and the existing method can reduce the average fitting error from 2.16% of installed capacity to 1.49% compared to the high-efficiency method. Although the proposed method is slower in solving speed than the high-efficiency method, it is significantly better than the unstable existing method. Full article

The main purposes of the present paper are to present the mathematical and algorithmic aspects of the ANM/FEM numerical model and to show how it is applied to analyze elastic and thermo-elastic nonlinear solid mechanical problems. ANM is a robust continuation method based on a perturbation technique for solving nonlinear problems dependent on a loading parameter. Historically, this technique has been successfully applied to problems in various fields of solid and fluid mechanics. This paper shows how ANM is used to solve nonlinear elastic and nonlinear thermo-elastic problems involving elastic behavior and geometrical nonlinearities. The implementation of ANM for FEM in the FreeFEM++ language is then presented. The FEM software development platform, called FreeFEM++, is structured to work with variational formulations and, therefore, is well adapted to implement ANM for instability problems in solid mechanics. In order to illustrate the great efficiency of FreeFEM++, scripts will be presented for computing the different steps of ANM continuation for solid elastic structures, considering simple geometries subjected to conservative loading. For the purpose of validation, the problem of a cantilever subjected to an applied force is presented. Next, the new numerical model is applied to study wrinkles appearing in a planar film/substrate system that is subjected to compressive surface forces at the lateral faces of the film. Finally, the model is applied to a spherical film/substrate system subjected to thermo-elastic shrinkage. In both cases, the ANM/FEM prediction method, together with a Newton–Riks correction (if needed), identifies the equilibrium paths efficiently, especially after the post-buckling regime. Full article

The aim of this manuscript is to introduce the fractional integral inequalities of H-H types via multiplicative (Antagana-Baleanu) A-B fractional operators. We also provide the fractional version of the H-H type of the product and quotient of multiplicative superquadratic and multiplicative subquadratic functions via the same operators. Superquadratic functions, have stronger convexity-like behavior. They provide sharper bounds and more refined inequalities, which are valuable in optimization, information theory, and related fields. The use of multiplicative fractional operators establishes a nonlinear fractional structure, enhancing the analytical tools available for studying dynamic and nonlinear systems. The authenticity of the obtained results are verified by graphical and numerical illustrations by taking into account some examples. Additionally, the study explores applications involving special means, special functions and moments of random variables resulting in new fractional recurrence relations within the multiplicative calculus framework. These contributions not only generalize existing inequalities but also pave the way for future research in both theoretical mathematics and real-world modeling scenarios. Full article

Motion perception is a fundamental function of the tactile system, essential for object exploration and manipulation. While human studies have largely focused on discrete or pulsed stimuli with staggered onsets, many natural tactile signals are continuous and rhythmically patterned. Here, we investigate whether phase differences between “simultaneously” presented, “continuous” amplitude-modulated vibrations can induce the perception of motion across fingertips. Participants reliably perceived motion direction at modulation frequencies up to 1 Hz, with discrimination performance systematically dependent on the phase lag between vibrations. Critically, trial-level confidence reports revealed the lowest certainty for anti-phase (180°) conditions, consistent with stimulus ambiguity as predicted by the mathematical framework. I propose two candidate computational mechanisms for tactile motion processing. The first is a conventional cross-correlation computation over the envelopes; the second is a probabilistic model based on the uncertain detection of temporal reference points (e.g., envelope peaks) within threshold-defined windows. This model, despite having only a single parameter (uncertainty width determined by an amplitude discrimination threshold), accounts for both the non-linear shape and asymmetries of observed psychometric functions. These results demonstrate that the human tactile system can extract directional information from distributed phase-coded signals in the absence of spatial displacement, revealing a motion perception mechanism that parallels arthropod systems but potentially arises from distinct perceptual constraints. The findings underscore the feasibility of sparse, phase-coded stimulation as a lightweight and reproducible method for conveying motion cues in wearable, motion-capable haptic devices. Full article

To address the issues of external unknown disturbances and roll motion in the tracking control of underactuated unmanned surface vehicle (USV) formation, a cooperative formation control method based on nonlinear model predictive control (NMPC) algorithm and finite-time disturbance observer is proposed. Initially, a tracking error model for the USV formation is established within a leader–follower framework, utilizing a four-degree-of-freedom (4-DOF) dynamic model to simultaneously account for roll motion and trajectory tracking. This error model is then approximately linearized and discretized. To mitigate the initial non-smoothness in the desired trajectories of the follower USVs, a tracking differentiator is designed to smooth the heading angle of the leader USV. Thereafter, a quasi-infinite horizon NMPC algorithm is developed, in which a terminal penalty function is constructed based on quasi-infinite horizon theory. Furthermore, a finite-time disturbance observer is developed to facilitate real-time estimation and compensation for unknown marine disturbances. The proposed method’s effectiveness is validated both mathematically and in simulation. Mathematically, closed-loop stability is rigorously guaranteed via a Lyapunov-based proof of the quasi-infinite horizon NMPC design. In simulations, the algorithm demonstrates superior performance, reducing steady-state tracking errors by over 80% and shortening convergence times by up to 75% compared to a conventional PID controller. These results confirm the method’s robustness and high performance for complex USV formation tasks. Full article

Power converters play an important role in incorporating renewable energy sources into power systems. Among different converter designs, Buck and Boost converters are popular, as they use fewer components and deliver cost savings and high efficiency. However, Boost converters are known as non–minimum phase systems, imposing harder constraints for designing a robust converter. Developing an efficient controller for these topologies can be difficult since they exhibit nonlinearity and distortion in high frequency modes. The Lyapunov-based Adaptive Backstepping Control (ABSC) technology is used to regulate suitable outputs for these structures. This approach is an updated version of the technique that uses the stability Lyapunov function to produce increased stability and resistance to fluctuations in real-world circumstances. However, in real-time situations, disturbances with larger ranges such as supply voltage changes, parameter variations, and noise may have a negative impact on the operation of this strategy. To increase the controller’s flexibility under more difficult working settings, the most appropriate first gains must be established. To solve these concerns, the ABSC’s performance is optimized using the Reinforcement Learning (RL) adaptive technique. RL has several advantages, including lower susceptibility to error, more trustworthy findings obtained from data gathering from the environment, perfect model behavior within a certain context, and better frequency matching in real-time applications. Random exploration, on the other hand, can have disastrous effects and produce unexpected results in real-world situations. As a result, we choose the Deep Deterministic Policy Gradient (DDPG) approach, which uses a deterministic action function rather than a stochastic one. Its key advantages include effective handling of continuous action spaces, improved sample efficiency through off-policy learning, and faster convergence via its actor–critic architecture that balances value estimation and policy optimization. Furthermore, this technique uses the Grey Wolf Optimization (GWO) algorithm to improve the initial set of gains, resulting in more reliable outcomes and quicker dynamics. The GWO technique is notable for its disciplined and nature-inspired approach, which leads to faster decision-making and greater accuracy than other optimization methods. This method considers the system as a black box without its exact mathematical modeling, leading to lower complexity and computational burden. The effectiveness of this strategy is tested in both modeling and experimental scenarios utilizing the Hardware-In-Loop (HIL) framework, with considerable results and decreased error sensitivity. Full article

Tire contact imprint characteristics and pressure distribution directly affect their lateral mechanical characteristics under rolling conditions, which are the key influencing factors for vehicle handling stability. Based on the nonlinear finite element method, an explicit dynamic model of radial tires is established using Abaqus, and its contact process is simulated through phased load transfer and kinematic inversion. The modified mathematical model of contact pressure distribution is introduced from the geometric evolution law of contact imprint and the nonlinear characteristics of contact pressure distribution. The corrected lateral force and aligning torque and contact imprint behavior are analyzed. The results show that in the low roll-angle range, with the increase in the roll angle, the contact imprint shrinks asymmetrically, the pressure center shifts to the outer shoulder of the roll direction, and the lateral force and aligning torque show linear growth characteristics. At the critical value ±8°, the growth rate is significantly slowed down due to the stress saturation effect of the shoulder area. The research analyzes the evolution mechanism of the lateral mechanical characteristics of the contact imprint geometry and pressure distribution drive tires under roll conditions, providing theoretical support for vehicle handling stability optimization and tire structure design. Full article

In this work, we introduce the conformabletriple Laplace–Sumudu transform (CTLST), a novel integral transform designed to solve both linear and nonlinear conformable FPDEs. This new approach builds on the recent development of the triple Laplace–Sumudu transform and incorporates the conformable derivative to extend its applicability to fractional models. We first present the foundational definitions and key properties of the CTLST, followed by its application to a variety of two- and three-dimensional conformable FPDEs. The effectiveness of the proposed method is demonstrated through several examples, where exact and approximate solutions are derived, illustrative 3D plots are presented, and symmetry analysis is employed to verify the obtained results. The CTLST provides a promising analytical tool for tackling complex conformable FPDEs in mathematical physics and engineering. Full article

This work presents the results of a research study focused on the development and evaluation of an algorithmic optimal control framework for energy-efficient operation of screw compressors in smart power systems. The proposed approach is based on the Pontryagin maximum principle (PMP), which enables the synthesis of a mathematically grounded regulator that minimizes the total energy consumption of a nonlinear electromechanical system composed of a screw compressor and a variable-frequency induction motor. Unlike conventional PID controllers, the developed algorithm explicitly incorporates system constraints, nonlinear dynamics, and performance trade-offs into the control law, allowing for improved adaptability and energy-aware operation. Simulation results obtained using MATLAB/Simulink confirm that the PMP-based regulator outperforms classical PID solutions in both transient and steady-state regimes. Experimental tests conducted in accordance with standard energy consumption evaluation methods showed that the proposed PMP-based controller provides a reduction in specific energy consumption of up to 18% under dynamic load conditions compared to a well-tuned basic PID controller, while maintaining high control accuracy, faster settling, and complete suppression of overshoot under external disturbances. The control system demonstrates robustness to parametric uncertainty and load variability, maintaining a statistical pressure error below 0.2%. The regulator’s structure is compatible with real-time execution on industrial programmable logic controllers (PLCs), supporting integration into intelligent automation systems and smart grid infrastructures. The discrete-time PLC implementation of the regulator requires only 10³ arithmetic operations per cycle and less than 10² kB of RAM for state, buffers, and logging, making it suitable for mid-range industrial controllers under 2–10 ms task cycles. Fault-tolerance is ensured via range and rate-of-change checks, residual-based plausibility tests, and safe fallbacks (baseline PID or torque-limited speed hold) in case of sensor faults. Furthermore, the proposed approach lays the groundwork for hybrid extensions combining model-based control with AI-driven optimization and learning mechanisms, including reinforcement learning, surrogate modeling, and digital twins. These enhancements open pathways toward predictive, self-adaptive compressor control with embedded energy optimization. The research outcomes contribute to the broader field of algorithmic control in power electronics, offering a scalable and analytically justified alternative to heuristic and empirical tuning approaches commonly used in industry. The results highlight the potential of advanced control algorithms to enhance the efficiency, stability, and intelligence of energy-intensive components within the context of Industry 4.0 and sustainable energy systems. Full article

The start-up process of water-distribution networks has been extensively investigated in recent years, particularly regarding the pressure surges that may occur during such transient events. In this context, researchers have concentrated on exploring physical formulations capable of describing the behaviour of the two interacting phases—water and air—typically resolved through numerical approaches. This paper presents an analytical solution to the nonlinear mathematical model governing the start-up of water pipelines containing a trapped air pocket. The model adopts the rigid water column approximation for the liquid phase and a polytropic gas law to account for the compressibility of the air. The resulting system can be formulated as a second-order nonlinear differential equation. The analytical approach consists of transforming the governing equation into a first-order linear ordinary differential equation, in which the square of the water front velocity is expressed as a function of the water column length. This transformation yields a closed-form solution expressed as a special integral series. The required integrals are evaluated using binomial expansions and incomplete gamma functions, enabling the derivation of a general solution valid within alternating intervals of monotonic motion. A practical application involving an 800 m pipeline is presented. Furthermore, the proposed solution is validated against experimental measurements, demonstrating the accuracy and effectiveness of the analytical approach in capturing the system’s transient behaviour. Full article

In recent years, numerical optimization, UAVs, and robot path planning have become hot research topics. Solving these fundamental artificial intelligence problems is crucial for further advancements. However, traditional methods struggle with complex nonlinear problems, prompting researchers to explore intelligent optimization algorithms. Existing approaches, however, still suffer from slow convergence, low accuracy, and poor robustness. Inspired by graduate students’ daily behavior, this paper proposes a novel intelligent optimization algorithm, the Graduate Student Evolutionary Algorithm (GSEA). By simulating key processes such as searching for research directions and concentrating on studies, a mathematical model of GSEA is established. The algorithm’s convergence behavior is analyzed qualitatively, and its performance is evaluated against competitive algorithms on the CEC2017 and CEC2022 test sets. Statistical tests confirm GSEA’s effectiveness and robustness. To further validate its practical applicability, GSEA is applied to UAV and robot path planning problems, with experimental results demonstrating its superiority in solving real-world optimization challenges. Full article

Heart Rate Variability (HRV) analysis allows for assessing autonomic control from the beat-by-beat dynamics of the time series of cardiac intervals. However, some HRV indices may strongly correlate with the mean heart rate, possibly flawed by the interpretation of HRV changes in terms of autonomic control. Therefore, this study aims to (1) investigate how HRV indices of fluctuation amplitude and multiscale complex dynamics of cardiac time series faithfully describe the autonomic control at different heart rates through a mathematical model of the generation of cardiac action potentials driven by realistically synthesized autonomic modulations; and (2) propose an alternative procedure of HRV analysis less sensitive to the mean heart rate. Results on the synthesized series confirm a strong dependency of amplitude indices of HRV on the mean heart rate due to a nonlinearity in the model, which can be removed by our procedure. Application of our procedure to real cardiac intervals recorded in different postures suggests that the dependency of these indices on the heart rate may importantly affect the physiological interpretation of HRV. By contrast, multiscale complexity indices do not substantially depend on the heart rate provided that multiscale analyses are defined on a time- rather than a beat-basis. Full article

This study investigates the mechanical behavior of water-washable photosensitive resins used in masked stereolithography (mSLA) 3D printing, evaluating the effect of post-curing time (0, 5, 10, 30, and 60 min) and printing orientation (Flat [XY], Vertical [Z], and On-edge [XZ]) on the material characteristics. Specimens were manufactured according to ISO 527-2 type 1B and ISO 178 standards for tensile and bending tests, respectively. A Matlab algorithm was developed to automate the processing of experimental data. This tool enabled the extraction of parameters to fit distinct mathematical models for the elastic (linear) and nonlinear (polynomial) regimes, allowing the material response to be characterized at different curing times and print orientations. These models were implemented in Ansys Workbench for comparison with experimental results. The results show that increasing the post-curing time from 0 to 60 min raises the elastic modulus from 964.5 to 1892.4 MPa in the Flat [XY] orientation and from 774 to 1661.2 MPa in the Vertical [Z] orientation for tensile testing. In bending testing, the Flat [XY] orientation presented the best mechanical properties, while the Vertical [Z] and On-edge [XZ] orientations showed similar behavior. The numerical simulations adequately reproduced the experimental results, validating the developed constitutive models. Finally, a stress–strain correlation model is presented that enables estimation for any post-curing time between 0 and 60 min. This study provides essential data for optimizing 3D printing processes and developing structural applications with photopolymer resins. Full article