Search Results (197)

A Lyapunov-based framework for stability analysis and synthesis of adaptive neural-network (NN) controllers for a class of uncertain second-order nonlinear systems (SNS) with bounded external perturbations and unmodelled dynamics is presented. Online learning is employed for the reconstruction of the plant nonlinearity with the use of a radial-basis-function (RBF) network whose weights are adapted using a direct adaptation law deduced from a single composite Lyapunov function. The proposed controller couples the weight update to a persistent robustifying action, while the closed-loop stability is guaranteed throughout the learning transient, in contrast to schemes that guarantee stability after learning has converged. Using a composite Lyapunov function in the filtered tracking error and the weight-estimation error, we prove that all closed-loop signals are uniformly ultimately bounded (UUB) and that the tracking error converges to an explicitly characterized residual set whose radius is governed by the network reconstruction accuracy, the disturbance bound and the design gains. A $\sigma$-modification ensures parameter boundedness without persistency of excitation, and a robustness theorem shows that bounded parametric perturbations of the plant preserve stability and enlarge the ultimate bound only gradually (a graceful degradation, rather than a loss of the guarantee). The open-loop plant (a forced double-well Duffing oscillator) is characterized by means of equilibrium and Jacobian analyses. A bifurcation diagram and the largest Lyapunov exponent are presented, which show a chaotic regime (with ${\lambda }_1\approx 0.17$). Numerical experiments indicate that the proposed controller is able to suppress the chaotic motion with a small value of the ultimate bound, and maintain a smooth reference motion with a small and constant RMS error of order ${10}^{-3}$, which is approximately 26 times less than the RMS error obtained with a tuned fixed-gain baseline, and the theoretical dependence of the ultimate bound on the disturbance and the design gains is confirmed by sensitivity sweeps. Full article

This paper investigates the constrained particle dynamics on rotational surfaces within the 4-dimensional pseudo-Euclidean space $E_2^4$, characterized by its second-order metric signature of index 2. A comprehensive Lagrangian and Hamiltonian formulation is developed to construct the specific energy and specific angular momentum as conserved Noetherian charges along timelike geodesics. By integrating Clairaut’s theorem into the geodesic flow equations, explicit analytical expressions for these fundamental physical invariants are obtained. This work explores the structural relationship between the surface’s continuous rotational symmetries and the mechanical stability of the geodesic flow. A mathematical resolution for the signature transitions manifested via the appearance of the imaginary unit i on elliptic surfaces is provided through analytic continuation and distinct coordinate charts. Furthermore, by reducing the second-order geodesic flow to a one-dimensional energy balance equation, the exact effective potentials ($V_{eff}$) are derived, and the local orbital stability zones are analytically verified via second-order radial derivatives (${\partial }_s^2{V}_{eff}>0$). These embedded geometric configurations are shown to share qualitative features with the equatorial slices of rotating relativistic spacetimes. Consequently, they can serve as potential geometric toy-models for studying the dynamics of photon spheres, ergosphere oscillations, and innermost stable circular orbits in extreme gravitational fields. Full article

To address high-precision trajectory tracking challenges in multi-joint robots facing model uncertainties, complex friction, and abrupt disturbances, this paper proposes a radial basis function (RBF) neural network-improved integral terminal sliding mode control scheme optimized by state-aware adaptive particle swarm optimization (ASPSO), denoted as ASPSO-optimized RBF-IITSMC. First, a fractional-memory integral terminal sliding surface incorporating a boundary-layer saturation mapping is constructed. The proposed terminal mapping is shown to be globally Lipschitz continuous, and an explicit approximation-error bound relative to the conventional terminal power mapping is established. Second, an RBF neural compensator driven by the sliding variable is incorporated into the reconstructed sliding dynamics to estimate lumped uncertainties and reduce the compensation burden on the robust feedback term. Furthermore, a state-aware adaptive PSO variant combining population-diversity monitoring and differential mutation is developed to jointly tune the 15-dimensional controller parameter vector. The practical finite-time reachability of the sliding variable and the uniform ultimate boundedness of the sliding variable and neural-weight estimation error are analyzed using a Lyapunov framework. Simulation results on a six-degree-of-freedom (6-DOF) robotic arm demonstrate improved tracking accuracy and disturbance-rejection performance, together with reduced high-frequency torque oscillations, compared with the evaluated baseline controllers. Full article

We model the compact object Cen X-3, which is considered to be a good strange quark star candidate of known mass and radius, incorporating a negative anisotropic factor, and we compute the frequencies of the ten lowest radial oscillation modes. We introduce the anisotropy in three different ways, and we investigate its impact on the spectra. Full article

To improve the energy conversion performance and long-term structural stability of stay vane mixed-flow chemical pumps used for industrial residual pressure recovery, this paper establishes a coupled numerical framework of computational fluid dynamics (CFD) and finite element structural analysis (FEA). The internal flow evolution, radial hydraulic excitation, transient pressure oscillation and impeller mechanical bearing capacity are systematically investigated under three typical flow states: partial load 0.7 Q_d, design condition 1.0 Q_d and overload 1.2 Q_d. The results show that the flow inside the pump is smooth and there is no obvious backflow or separation under the rated working condition, and the energy conversion efficiency is the best. When operating under partial discharge, boundary layer separation and recirculating secondary vortices easily emerge inside the pump passage, which drastically elevates hydraulic energy dissipation. Meanwhile, operating load exerts a remarkable influence on the impeller’s radial hydraulic load and transient pressure oscillation intensity. The radial force and the pressure pulsation amplitude at the impeller outlet are the largest under the small flow condition, and the force is the most stable under the rated working condition. Blade passing frequency dominates the frequency components of transient pressure fluctuations. The maximum von-Mises stress on the impeller concentrates at the filet where blade roots connect with the hub, and this peak value hits 86.3 MPa under partial-load low-flow operating status. Calculated stress values for all three flow rates satisfy the structural safety criteria. The outcomes of this numerical investigation can offer reliable technical support for hydraulic performance optimization and structural dimension design of this type of mixed-flow chemical pump. Full article

In complex environments, tower cranes not only need to efficiently transport loads to specified target points but also must avoid obstacles present in their surroundings. This poses a significant challenge for the load positioning control of tower cranes. To tackle this problem, an accurate model-based approach is developed for trajectory planning and tracking control, enabling both obstacle avoidance and precise load positioning during the crane’s lifting process. Specifically, the paper formulates smooth parameterized load trajectories in the tower crane task space using piecewise Bézier curves. The positions of curve control points are designed to allow independent adjustment of each trajectory segment, thus avoiding obstacles during load movement and ensuring operational safety. A novel method for defining the load swing angle is introduced, which employs the system’s differential flatness to map the smooth parameterized trajectories from the task space to the system’s generalized state space without requiring model linearization, thereby ensuring the designed trajectories’ precision and traceability. A meticulously designed high-order sliding mode controller is employed to ensure the jib and trolley accurately follow the prescribed reference trajectory, while effectively suppressing load swing angle, thereby achieving precise load positioning. Finally, the proposed control strategy was tested on a tower crane experimental platform. Experimental validation reveals that the maximum radial swing angle is limited to 3.264°, while the maximum slew swing angle reaches 3.599°, with residual oscillations reduced to 0.425° and 0.343°, respectively. Compared with conventional input-shaping methods, the maximum radial swing and residual oscillation are reduced by 72.7% and 88.9%, respectively. These results demonstrate that the designed trajectory planning and tracking control strategy enables the tower crane load to avoid obstacles smoothly and position precisely at the target point. Full article

Unsteady laminar pipe flows, prevalent in oscillating liquid columns, physiological pulsatile systems, and hydraulic transients, exhibit instantaneous velocity distributions that deviate significantly from the classical Hagen–Poiseuille parabolic profile. This deviation is governed by the interaction of inertial effects, viscous diffusion, phase lags, and localized flow reversal. Despite extensive documentation of these phenomena, a systematic framework for quantifying such morphological deviations remains largely undeveloped. This study proposes a suite of physically grounded indicators to quantify velocity profile distortion. These metrics characterize complementary aspects of non-Poiseuillean behavior, specifically: centerline curvature variation, profile flattening, energetic divergence, radial peak migration, reverse-flow fraction, and the emergence of inflection points. The methodology employs an analytical reconstruction of the local velocity field through a generalized Fourier–Bessel solution of the linearized Navier–Stokes equations, calibrated against experimental free-surface motion in a vertical U-tube undergoing damped oscillations. The application of these indicators demonstrates consistent correlations between geometric, energetic, and topological features during acceleration, deceleration, and flow-reversal phases. The findings indicate that no single parameter adequately captures the complexity of unsteady fields, but the integrated framework provides a robust classification of instantaneous flow regimes. This approach delineates the limitations of Poiseuille-based assumptions and establishes a quantitative foundation for advanced unsteady friction models. Full article

This paper proposes a hybrid SMC + ESO + RBF control architecture designed to evaluate trajectory tracking and liquid sloshing suppression in tanker robots navigating complex terrains within a simulated environment. A multi-variable dynamic model integrates the differential drive mobile platform with an equivalent mass-spring-damper sloshing system under terrain disturbances. To achieve robust stability, an Extended State Observer (ESO) neutralizes baseline generalized disturbances, while a Radial Basis Function (RBF) neural network adaptively compensates for residual nonlinear coupled sloshing errors. Practical stability and uniform ultimate boundedness (UUB) of the closed-loop system are proven via Lyapunov theory under bounded network approximation errors and observer uncertainties. Numerical simulations in MATLAB/Simulink demonstrate that the proposed controller achieves a baseline Root Mean Square Error (RMSE) of 0.0109 m, representing an 84.1% improvement over traditional Sliding Mode Control (SMC). Parametric sensitivity analysis under variable liquid filling ratios (30%, 50%, and 70%) and a circular steering topology indicates notable adaptability, with the tracking RMSE bounded between 0.0085 m and 0.0129 m under the considered virtual scenarios. Within the simulated environment, the system successfully smooths control profiles and dampens liquid oscillations, demonstrating a promising potential to support transport safety and mitigate actuator chattering under virtual constraints. However, these qualitative observations serve as preliminary hypotheses and must be formally verified through future hardware-in-the-loop (HIL) experiments to evaluate the impact of physical non-idealities, including sensor noise, actuator saturation, communication delays, and wheel slip. These findings confirm the competitive analytical robustness of the SMC + ESO + RBF framework in stabilizing tanker robots within highly uncertain simulated operational environments. Full article

To improve the operational stability and mass transfer performance of fluidized bed reactors under dynamic conditions, this study examines radial particle velocity distributions at different bed cross-sections using a dual-probe measurement method across a range of rocking frequencies and superficial gas velocities. The analysis identifies the dominant influence of additional inertial forces generated by rocking motion, including the Euler force and Coriolis force, in determining the time-averaged flow structure, leading to the development of a spatiotemporally averaged flow field model and clarification of the interaction mechanisms between these forces. Results indicate that the flow field exhibits two representative macroscopic patterns governed by the interplay between inertial forcing and particle response characteristics: at low frequencies, the slowly varying Euler force combines with gravity to produce a coherent large-scale single-circulation structure, whose stability is sustained under higher gas velocities due to reduced internal energy dissipation associated with stronger drag; at high frequencies, the Coriolis force promotes structural division while the rapidly oscillating Euler force introduces disturbances, resulting in the formation and persistence of double or multi-circulation flow structures under their combined action. Full article

This paper investigates a tracking control problem for a class of strict-feedback nonlinear systems with time delays, asymmetric output constraints, and deception attacks on the controller. First, by introducing a new error conversion technology, any nonzero and bounded initial state is converted to zero, which not only solves the overshoot/oscillation problem of the output during the constraint switching phase but also unifies the control design of constrained and unconstrained systems. Second, a barrier function with asymmetric output constraints is designed, which converts the problem of satisfying the tracking control of nonlinear systems under output constraints into one of ensuring the boundedness. In addition, radial basis function neural networks (RBFNNs) are utilized to handle both unknown uncertain terms and deception attacks simultaneously. By utilizing the new asymmetric delayed barrier function error together with an RBFNN technique, the tracking error is ultimately uniformly bounded, regardless of the presence or absence of output constraints. Finally, the superiority of the proposed strategy is verified through its simulation on an unmanned aerial vehicle (UAV) system. Full article

We study the quantitative structure of the reciprocity gap method for inclusions with spatially varying conductivity. Motivated by the variable-coefficient reciprocity gap identity, we investigate the discrete approximation mechanism underlying the bounded/blow-up dichotomy for sampling points inside and outside the inclusion. The reciprocity gap functional is discretized by harmonic test functions, and the resulting ill-conditioned linear system is regularized by a Tikhonov term consistent with the $L^2(\partial D)$ trace norm appearing in the weighted formulation. The regularization parameter is selected by the L-curve criterion. For constant, radially varying, and angularly oscillating contrasts, the numerical results show that exterior sampling points exhibit an approximately exponential growth of $\parallel v_N{\left(z\right)\parallel }_{L^2(\partial D)}$ with respect to the harmonic order N, whereas interior points remain bounded. This behavior is quantified through fitted growth rates and contrast indicators, and its dependence on geometry and model parameters is examined. The results provide a quantitative description of the reciprocity gap approximation mechanism in heterogeneous media and show that the bounded/blow-up dichotomy remains numerically detectable beyond the constant-coefficient setting. Full article

Contact–impact phenomena caused by joint clearances can significantly alter the dynamic response of high-speed mechanical systems, yet fewer studies combine analytical impact-force modeling, virtual prototyping, and experimental observations for multi-cylinder internal combustion engine mechanisms within a unified framework. This problem is scientifically important because the piston–connecting rod–crankshaft chain is subjected to rapid motion reversals, high transmitted loads, and local clearances that may generate shocks, force amplification, and vibration growth. The objective of this study is to evaluate the influence of mechanical impact on the dynamic response of a three-cylinder inline engine mechanism by combining analytical modeling, MSC Adams virtual prototyping, and experimental investigation. The mechanism was analyzed in two operating conditions: under load, using an experimentally derived gas pressure input, and without load at low speed imposed on the crankshaft, using a sectioned engine test bench. The loaded virtual model was studied at a crankshaft speed of 6000 rpm, with cylinder gas pressure peaks above 90 bar and engine torque oscillating around 170 Nm. A radial clearance of 0.03 mm was introduced in the connecting rod–piston joint to evaluate clearance-induced impacts. The results showed that the damping coefficient strongly influences the amplitude and harmonic content of the impact force. For the analyzed no-load case at low speed, the simulated impact force reached a maximum value of 3000 N. Experimentally, the worn connecting rod with 0.03 mm clearance exhibited markedly higher dynamic response than the clearance-free case, with the maximum longitudinal acceleration increasing from 17.77 to 48.26 m/s² at 1.341 Hz. The novelty of the study lies in the integrated analytical–virtual–experimental investigation of clearance-induced impact in a three-cylinder inline engine mechanism and in the comparative evaluation of its effects on joint forces and vibration signatures. In addition, compared to other models, the novelty lies in introducing and adapting the impact force damping component for mechanisms with rapid motion and high dynamic loads. Full article

Nonlinear model predictive control (NMPC) delivers high tracking accuracy for industrial processes but requires solving a nonlinear program at each sampling instant, limiting its applicability under tight real-time constraints. The Koopman operator provides a principled route to circumvent this limitation by embedding nonlinear dynamics into a higher-dimensional space where the evolution becomes linear, thereby reducing the online optimization to a convex quadratic program. This paper presents a Koopman-based MPC framework (K-MPC) that incorporates three algorithmic contributions. First, an adaptive radial basis function dictionary learning procedure selects lifting functions from process data, eliminating manual basis selection and improving approximation fidelity for systems with localized nonlinearities. Second, a recursive least-squares update rule adjusts the Koopman matrix online as new measurements arrive, enabling the controller to track slow parameter drifts without full model recomputation. Third, a tube-based constraint tightening strategy accounts for the residual linearization error, preserving recursive feasibility under bounded Koopman approximation mismatch. Simulations on a Van der Pol oscillator, a continuous stirred-tank reactor (CSTR), and a four-state Tennessee Eastman-inspired distillation column demonstrate that K-MPC achieves root-mean-square tracking errors within 11–16% of NMPC while reducing average per-step computation time by a factor of 14 to 18. The recursive update mechanism reduces prediction error by 80% compared to the fixed offline Koopman model when reactor feed concentration drifts by 15% from its nominal value. Ablation experiments confirm that adaptive dictionary learning and online updating each contribute measurably to closed-loop performance. Full article

The results of the development and practical application of a comprehensive system for studying gear cutting processes are presented. The processes are traditional hobbing, modern power skiving, and radial-circular methods. Carrying out these processes is based on the gear teeth continuous generating method using complex kinematics. This complicates the analysis, description and modeling of the processes. The developed system provides for a logical sequence of step-by-step modeling and simulation of interrelated processes and phenomena accompanying gear processing. Reproducing volumetric chips and calculating their parameters provides the basis for determining deformation and contact processes, cutting forces, elastic deformations, machining accuracy and energy costs per operation. After establishing the operation to overcome friction and heat flows, the degree of heating and the temperature of the working surfaces are calculated to predict tool wear and its service life. Based on the parametric non-uniformity of the considered processes, the intensity of oscillations and vibrations of gear cutting machines is predicted, and their impact on the quality of gear surfaces and the accuracy of gears is determined. These approaches enable the study of such processes at the level of individual teeth and blades during cutting. They also allow gear cutting technology and cutting tools to be optimized according to the most important criteria and performance assessments. Full article

This study presents a mathematical model of the dynamics of a cavitation bubble oscillating near a rigid wall under an electromagnetic field. The model utilizes a modified Keller–Miksis equation incorporating the compressibility effects of the surrounding Newtonian conducting fluid. The rigid boundary’s effects, modeled using the image method, contributed to an additional pressure, which altered the cavitation bubble’s radial dynamics. Electromagnetic effects were incorporated through the Maxwell stresses induced by an external electric field, electrostatic pressure from surface charge accumulated at the bubble’s interface, and magnetic damping arising from the electric currents induced in the conducting fluid. The resulting nonlinear ordinary differential equation was solved using a fourth- and fifth-order Runge–Kutta scheme. Validation against previous theoretical and experimental studies showed good agreement, confirming the model’s reliability. A parametric analysis showed that the bubble–wall distance, electric field intensity, magnetic field strength, and surface charge magnitude considerably influence the behaviors of oscillating bubbles. Electric fields and surface charges promote bubble expansion, whereas magnetic fields and nearby surfaces restrict its size, thereby influencing its collapse. These behaviors can be attributed to the governing equation and the magnitude of its nonlinear terms. The proposed model provides a consistent mathematical framework for analyzing the electro-magnetohydrodynamic cavitation phenomena near rigid boundaries. Full article