Search Results (470)

The complex analytic continuation can be developed to enable the Gauss-Krüger projection to be non-zonal and non-singular in polar regions. The series expansion of the traditional Gauss-Krüger projection in terms of third flattening has been derived by using a computer algebra system, leading to a substantial simplification of the final formulas without compromising accuracy compared with the series expansion in terms of eccentricity. Therefore, the non-zonal formulas of the Gauss-Krüger projection in term of third flattening have been expressed, and the non-zonal and the non-singular formulas of the Gauss-Krüger projection has been derived by the conformal colatitude. With respect to the mapping of 4 high-latitude regions (Finland, Sweden, Norway and Alaska) and its isopleth map, it was verified that the non-zonal and the non-singular algorithm of the Gauss-Krüger projection had high precision and minimal distortion in polar regions. The method presented a meaningful supplement to the existing Gauss–Krüger projection family. Full article

Quadrotor UAVs benefit from control strategies that can deliver rapid convergence and strong robustness in order to fully exploit their high agility. Finite-time control based on terminal sliding modes has been recognized as an effective alternative to classical sliding mode control, which only guarantees asymptotic convergence. Its enhanced variant, nonsingular fast terminal sliding mode control, eliminates singularities and achieves accelerated convergence; however, chattering-induced high-frequency oscillations remain a major concern. To address this issue, this study introduces a hybrid control framework that combines the super-twisting algorithm with ${\mathcal{L}}_1$ adaptive control. The super-twisting component preserves the robustness of sliding mode control while mitigating chattering, whereas ${\mathcal{L}}_1$ adaptive control provides rapid online estimation and compensation of model uncertainties and unknown disturbances. The resulting scheme is implemented in a quadrotor flight-control architecture and evaluated through numerical simulations. The results show that the proposed controller offers faster convergence and enhanced robustness relative to existing approaches, particularly in the presence of wind perturbations, periodic obstacle-avoidance maneuvers, and abrupt partial loss of propeller thrust. Full article

This paper develops a unified synchronization framework for octonion-valued fractional-order neural networks (FOOVNNs) subject to mixed delays, Lévy disturbances, and topology switching. A fractional sliding surface is constructed by combining $I^{1-\mu }{e}_g$ with integral terms in powers of $|e_g|$. The controller includes a nonsingular term $-{\rho }_{2g}{s}_g^{c_2}\mathrm{sign}\left(s_g\right)$, a disturbance-compensation term $-{\widehat{\theta }}_g\mathrm{sign}\left(s_g\right)$, and a delay-feedback term $-{\lambda }_g{e}_g(t-\tau )$, while dimension-aware adaptive laws ${\phantom{,}}^C{D}_t^{\mu }{\rho }_g=k_{1g}N{\parallel s_g\parallel }^{c_2}$ and ${\phantom{,}}^C{D}_t^{\mu }{\widehat{\theta }}_g=k_{2g}N\parallel s_g\parallel$ ensure scalability with network size. Fixed-time convergence is established via a fractional stochastic Lyapunov method, and predefined-time convergence follows by a time-scaling of the control channel. Markovian switching is treated through a mode-dependent Lyapunov construction and linear matrix inequality (LMI) conditions; non-Gaussian perturbations are handled using fractional Itô tools. The architecture admits observer-based variants and is implementation-friendly. Numerical results corroborate the theory: (i) Two-Node Baseline: The fixed-time design drives ${\parallel e\left(t\right)\parallel }_1$ to $\mathcal{O}\left({10}^{-4}\right)$ by $t\approx 0.94\mathrm{s}$, while the predefined-time variant meets a user-set $T_p=0.5\mathrm{s}$ with convergence at $t\approx 0.42\mathrm{s}$. (ii) Eight-Node Scalability: Sliding surfaces settle in an $\mathcal{O}\left(1\right)$ band, and adaptive parameter means saturate well below their ceilings. (iii) Hyperspectral (Synthetic): Reconstruction under Lévy contamination achieves a competitive PSNR consistent with hypercomplex modeling and fractional learning. (iv) Switching Robustness: under four modes and twelve random switches, the error satisfies ${max}_t{\parallel e\left(t\right)\parallel }_1\le 0.15$. The results support octonion-valued, fractionally damped controllers as practical, scalable mechanisms for robust synchronization under non-Gaussian noise, delays, and time-varying topologies. Full article

This paper introduces a novel control framework for prescribed-time synchronization of higher-order nonlinear multi-agent systems (MAS) subject to parametric uncertainties and external disturbances. The proposed method integrates a fuzzy neural network (FNN) with a robust non-singular terminal sliding mode controller (NTSMC) to ensure leader–follower consensus within a user-defined time horizon, regardless of the initial conditions. The FNN is employed to approximate unknown nonlinearities online, while an adaptive update law ensures accurate compensation for uncertainty. A terminal sliding manifold is designed to enforce finite-time convergence, and Lyapunov-based analysis rigorously proves prescribed-time stability and boundedness of all closed-loop signals. Simulation studies on a leader–follower MAS with four nonlinear agents under directed communication topology demonstrate the superiority of the proposed approach over conventional sliding mode control, achieving faster convergence, enhanced robustness, and improved adaptability against system uncertainties and external perturbations. Full article

A fast and stable flight control system is crucial for improving the efficiency of unmanned aerial vehicle (UAV) missions. Focusing on the trajectory tracking control of quadrotor UAVs, this paper proposes a trajectory tracking control method based on the global fast terminal sliding mode control (GFTSMC) algorithm to address the slow response speed and insufficient anti-disturbance capability inherent in the widely used Proportional–Integral–Derivative (PID) control algorithm and conventional sliding mode control (SMC) algorithm. Firstly, considering the gyroscopic moment of a quadrotor UAV’s rotors, an accurate kinematic and dynamic model of a quadrotor UAV is established, and the trajectory tracking problem faced by such UAVs is decoupled into the command tracking problems of the position loop and the attitude loop. Secondly, GFTSMC controllers are designed for these loops, and the Lyapunov principle is adopted to prove the stability of the designed controllers. Finally, simulation verification is carried out. The simulation results show that, compared to PID control, GFTSMC-based trajectory tracking control for quadrotor UAVs exhibits the characteristics of no overshoot, higher tracking accuracy, and stronger anti-disturbance capability. Compared to nonsingular terminal sliding mode control (NTSMC) and SMC, GFTSMC-based trajectory tracking control reduces the steady-state convergence time by 33.8% and 36.5% and the steady-state disturbance error by 83.1% and 97.3%, respectively, demonstrating faster response speed and stronger anti-disturbance capability. Therefore, the application of GFTSMC significantly improves the trajectory tracking control performance of quadrotor UAVs, thereby supporting them in performing operations in scenarios requiring high real-time performance, precision, and anti-disturbance capability. Full article

Most control strategies for magnetic bearings are typically formulated upon the linearized suspension force model, and the nonlinear characteristics are neglected or regarded as the disturbance and variation in parameters of the control system. The controllers based on linearized suspension force model struggle to achieve fast response under disturbance. Therefore, a nonlinear mathematic model that simultaneously represents the main nonlinearity of suspension force and facilitates the design of high-performance controller is necessary to establish. In this study, a new mathematical model of suspension force with varying current stiffness is developed, and a specific controller was designed based on this model. Firstly, the nonlinear mathematical model of six-pole radial–axial hybrid magnetic bearing (RAHMB) is established. Secondly, the characteristics of the current stiffness varying with rotor displacement are analyzed and the expression between current stiffness and rotor displacement is fitted. Then, the linearized model is built via Taylor expansion of the nonlinear model. Subsequently, the varying current stiffness model is constructed by substituting the fitted expression of varying current stiffness into linearized model. Finally, an adaptive nonsingular terminal sliding mode controller (ANTSMC) is designed based on the proposed varying current stiffness model. The simulation and experiment results have shown that the ANTSMC based on varying current stiffness model reduces chattering more than 64% and reduces convergence time more than 70% to the NTSMC based on the linearized model. Full article

To address the challenges of low control accuracy and poor robustness for pipe robots operating in complex environments with compound uncertainties, including parameter variations, nonlinear friction, and external disturbances, this paper proposes an integrated adaptive robust control strategy. The framework begins by establishing a high-fidelity dynamic model that considers arbitrary pipe inclination. Subsequently, a Finite-Time Disturbance Observer (FTDO) is designed to rapidly and accurately estimate and compensate for the lumped uncertainties, thereby enhancing the system’s disturbance rejection capabilities. Based on this compensation, an Adaptive Non-singular Terminal Sliding Mode Control (ANTSMC) law is synthesized. By adjusting its gain online, the controller handles unknown uncertainty bounds, ensures the finite-time convergence of tracking errors, and effectively suppresses chattering. Simulation results validate that the proposed method achieves high-precision trajectory tracking with smooth control inputs and strong robustness, even in the presence of significant uncertainties. This study offers an effective solution for the high-precision and robust motion control of pipe robots. Full article

This paper presents an approach to the velocity control loop of induction motor drives utilizing the Higher-Order PID-Nested Nonsingular Terminal Sliding Mode (PID-NTSM) method. Here, the PID-NTSM sliding manifold is formulated by the incorporation of both derivative and integral errors of states into the conventional nonsingular terminal sliding mode surface (NTSM). In this manner, the control signals take the higher-order sliding mode control law, obtained by multiple integrals. In this way, such signals are continuous, and the sliding manifold is obtained in finite time; the system’s states asymptotically converge chattering-free to zero at a much faster response time and higher tracking precision while maintaining inherited robustness characteristics. The effectiveness of the proposed method is comprehensively validated both numerically and experimentally. Full article

This paper introduces a singular distance function r_s in terms of a symmetric non-negative metric tensor S. If S satisfies a quadratic matrix equation involving a parameter β, then for the Laplace equation $r_s^{\beta }$ is a non-singular generalized radial basis function solution if 2 > β > 0, and a weaker singularity fundamental solution if −1 < β < 0. With a unit vector as a medium to express S, we can derive the metric tensor in closed form and prove that S is a singular projection operator. For the anisotropic Laplace equation, the corresponding closed-form representation of S is also derived. The concept of non-singular generalized radial basis function solution for the Laplace-type equations is novel and useful, which has not yet appeared in the literature. In addition, a logarithmic type method of fundamental solutions is developed for the anisotropic Laplace equation. Owing to non-singularity and weaker singularity of the bases of solutions, numerical experiments verify the accuracy and efficiency of the proposed methods. Full article

This paper presents a composite control strategy for gearless coal mill to improve the disturbance immunity under low-speed variable operating conditions. First, the gearless coal mill encounters power supply voltage fluctuations, mechanical failures, or ambient temperature changes during operation. These situations can cause the system to suffer from the problem of insufficient control accuracy of the rotational speed. Therefore, a non-singular fast terminal sliding mode control strategy is proposed to improve the speed response. Then, to address the problem of load perturbation caused by different coal quality, this paper designs the extended state observer. Feed-forward compensation of the perturbation is performed to improve the robustness. Finally, due to the parameter mismatch problem caused by heat in operations that take a long time, this paper proposes a sliding-mode-based deadbeat predictive current control. The strategy possesses the fast dynamic response of deadbeat predictive current control while retaining the strong robustness of sliding mode control. Lyapunov proved the stability of the proposed control strategy. The experimental results verified that the proposed control strategy had better control performance. Full article

This study investigates three distinct charged gravastar models within the framework of $f\left(T\right)$ modified gravity, considering the functional forms $f\left(T\right)=T$, $f\left(T\right)=a+bT$, and $f\left(T\right)=T^2$. Inspired by the Mazur–Mottola conjecture, we propose these models as singularity-free alternatives to black holes, each characterized by a three-region structure: (i) an interior de Sitter core, (ii) an intermediate thin shell composed of ultrarelativistic matter, and (iii) an exterior region described by the Reisner Nordstrom solution and other novel spherically symmetric vacuum solutions. We derive a complete set of exact, singularity-free solutions for the charged gravastar configuration, demonstrating their mathematical consistency and physical viability in the context of alternative gravity theories. Notably, the field equations governing the thin shell are solved using an innovative approach based on Killing vector symmetries, eliminating the need for approximations commonly employed in prior studies. Furthermore, we analyze key physical properties of the thin shell, including its proper length, entropy distribution, and energy content. A thorough examination of the energy conditions reveals the thermodynamic stability and viability of these models. Our results contribute to the growing body of work on exotic compact objects and provide new insights into the interplay between modified gravity, electromagnetism, and non-singular black hole alternatives. Full article

In this paper, the symmetric character of the thermal conductivity tensor for anisotropic materials is established based on arguments from tensor analysis and the physical constraints on the domain of definition of the conductivity tensor. The non-singular nature of the conductivity tensor plays a fundamental role in demonstrating not only its symmetry but also its positive definiteness. Full article

In this work, we numerically investigate the fractional clannish random walker’s parabolic equations (FCRWPEs) and the nonlinear fractional Cahn–Allen (NFCA) equation using the Hybrid Decomposition Method (HDM). The analysis uses the Atangana–Baleanu fractional derivative (ABFD) in the Caputo sense, which has a nonsingular and nonlocal Mittag–Leffler kernel (MLk) and provides a more accurate depiction of memory and heredity effects, to examine the dynamic behavior of the models. Using nonlinear analysis, the uniqueness of the suggested models is investigated, and distinct wave profiles are created for various fractional orders. The accuracy and effectiveness of the suggested approach are validated by a number of example cases, which also support the approximate solutions of the nonlinear FCRWPEs. This work provides significant insights into the modeling of anomalous diffusion and complex dynamic processes in fields such as phase transitions, biological transport, and population dynamics. The inclusion of the ABFD enhances the model’s ability to capture nonlocal effects and long-range temporal correlations, making it a powerful tool for simulating real-world systems where classical derivatives may be inadequate. Full article

This paper considers non-singular black holes. It discusses the observation of particles falling onto ordinary and non-singular black holes from the perspective of a distant observer. It is demonstrated that, during a stage in the evolution of non-singular black holes, powerful energy fluxes can be emitted. Distant observers may interpret these fluxes as white holes. Full article

This paper presents a rigid–flexible coupling dynamic modeling framework and a fixed-time control strategy for a flexible space-tethered satellite (STS) system. A high-fidelity rigid–flexible coupling dynamic model of STS is developed using the finite element method, accurately capturing the coupled attitude dynamics of the satellite platform and flexible tether. Leveraging a simplified representation of the STS model, a nonsingular terminal sliding-mode controller (NTSMC) is synthesized via fixed-time stability theory. Uncertainties and disturbances within the system are compensated for by a radial basis function neural network (RBFNN), ensuring strong robustness. The controller’s fixed-time convergence property—with convergence time independent of initial conditions—is established using Lyapunov stability theory, enabling reliable operation in complex space environments. Numerical simulations implemented on the STS rigid–flexible coupling model validate the controller’s efficacy. Comparative analyses demonstrate superior tracking performance and enhanced practicality over conventional sliding-mode controllers, especially in the aspect of chattering suppression for the satellite thrusters. Full article