Search Results (53)

Real-time computational capability for simultaneous grasping force and displacement determination constitutes a critical enabler for stable and reliable grasping performance in dexterous robotic grasping. To accelerate the computational efficiency of LCP in the dexterous grasping problem, as well as to ensure the stability and reproducibility of the algorithm’s output, the NSNMGK method, which incorporates sequential projection iterations across all greedy-selected active constraint rows within each NSNGRK framework iteration cycle, is developed. In each NSNMGK iteration, sequential projection operations are systematically applied to all active constraint rows, satisfying the greedy criterion. This processing strategy ensures the full utilization of qualifying constraints within the greedy subset through a same generalized Jacobian evaluation per iteration cycle. The methodology effectively mitigates inherent limitations of conventional randomized row selection, including unpredictable iteration counts and computational overhead from repeated Jacobian updates, while maintaining deterministic convergence behavior. The method’s convergence theory is rigorously established, with benchmark analyses demonstrating marked improvements in computational efficiency over the NSNGRK framework. Experimental validation in dexterous robotic grasping scenarios further confirms enhanced convergence rates through reduced iteration counts and shortened computational durations relative to existing approaches. Full article

Achieving high-order accuracy in finite difference/spectral methods for space-time fractional differential equations often relies on very restrictive and usually unrealistic smoothness assumptions in the spatial and/or temporal domains. For spatial discretization, spectral methods using smooth basis functions are commonly employed. However, spatial–fractional derivatives pose challenges, as they often lack guaranteed spatial smoothness, requiring non-smooth basis functions. In the temporal domain, finite difference schemes on uniformly graded meshes are commonly employed; however, achieving accuracy remains challenging for non-smooth solutions. In this paper, an efficient algorithm is adopted to improve the accuracy of finite difference/Pertrov–Galerkin spectral schemes for a time-space fractional reaction–diffusion equation, with a hyper-singular integral fractional Laplacian and non-smooth solutions in both time and space domains. The Pertrov–Galerkin spectral method is adapted using non-smooth generalized basis functions to discretize the spatial variable, and the L1 scheme on a non-uniform graded mesh is used to approximate the Caputo fractional derivative. The unconditional stability and convergence are established. The rate of convergence is $O\left(N^{\mu -\gamma }+K^{-min\{\rho \beta ,2-\beta \}}\right),$ achieved without requiring additional regularity assumptions on the solution. Finally, numerical results are provided to validate our theoretical findings. Full article

The calculation of grasping force and displacement is important for multi-fingered stable grasping and research on slipping damage. By linearizing the friction cone, the robot multi-fingered grasping problem can be represented as a linear complementarity problem (LCP) with a saddle-point coefficient matrix. Because the solution methods for LCP proposed in the field of numerical computation cannot be applied to this problem and the Pivot method can only be used for solving specific grasping problems, the LCP is converted into a non-smooth system of equations for solving it. By combining the Newton method with the subgradient and Kaczmarz methods, a Newton–subgradient non-smooth greedy randomized Kaczmarz (NSNGRK) method is proposed to solve this non-smooth system of equations. The convergence of the proposed method is established. Our numerical experiments indicate its feasibility and effectiveness in solving the grasping force and displacement problems of multi-fingered grasping. Full article

Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power-procurement schedule to minimize operating expenditure and the carbon footprint of cellular wireless networks equipped with energy-storage capacity, and hybrid energy systems comprising uncertain renewable energy sources. Despite the stochastic nature of wireless fading channels, the network operator must ensure a certain quality-of-service (QoS) constraint with high probability. This probabilistic constraint prevents using the dynamic programming principle to solve the stochastic optimal control problem. This work introduces a novel time-continuous Lagrangian relaxation approach tailored for real-time, near-optimal energy procurement in cellular networks, overcoming tractability problems associated with the probabilistic QoS constraint. The numerical solution procedure includes an efficient upwind finite-difference solver for the Hamilton–Jacobi–Bellman equation corresponding to the relaxed problem, and an effective combination of the limited memory bundle method (LMBM) for handling nonsmooth optimization and the stochastic subgradient method (SSM) to navigate the stochasticity of the dual problem. Numerical results, based on the German power system and daily cellular traffic data, demonstrate the computational efficiency of the proposed numerical approach, providing a near-optimal policy in a practical timeframe. Full article

In this paper, we propose a new finite-difference method for nonconvex absolute value equations. The nonsmooth unconstrained optimization problem equivalent to the absolute value equations is considered. The finite-difference technique is considered to compose the linear programming subproblems for obtaining the search direction. The algorithm avoids the computation of gradients and Hessian matrices of problems. The new finite-difference parameter correction technique is considered to ensure the monotonic descent of the objective function. The convergence of the algorithm is analyzed, and numerical experiments are reported, indicating the effectiveness by comparison against a state-of-the-art absolute value equations. Full article

Commonly used methods for identifying modal parameters under environmental excitations assume that the unknown environmental input is a stationary white noise sequence. For large-scale civil structures, actual environmental excitations, such as wind gusts and impact loads, cannot usually meet this condition, and exhibit obvious non-stationary and non-white-noise characteristics. The theoretical basis of the stochastic subspace method is the state-space equation in the time domain, while the state-space equation of the system is only applicable to linear systems. Therefore, under non-smooth excitation, this paper proposes a stochastic subspace method based on RDT. Firstly, this paper uses the random decrement technique of non-stationary excitation to obtain the free attenuation response of the response signal, and then uses the stochastic subspace identification (SSI) method to identify the modal parameters. This not only improves the signal-to-noise ratio of the signal, but also improves the computational efficiency significantly. A non-stationary excitation is applied to the spatial grid structure model, and the RDT-SSI method is used to identify the modal parameters. The identification results show that the proposed method can solve the problem of identifying structural modal parameters under non-stationary excitation. This method is applied to the actual health monitoring of stadium grids, and can also obtain better identification results in frequency, damping ratio, and vibration mode, while also significantly improving computational efficiency. Full article

Motor railway vehicles necessitate enhanced control of wheel-rail contact mechanics to ensure optimal adhesion. During train running, driving wheelsets exhibit torsional vibrations that compromise adhesion and potentially lead to axle damage. Consequently, the development of dynamic models for analyzing driving wheelset stick-slip phenomena and control strategies is an area of significant research interest for traction control, studies on rail corrugation, and locomotive drivetrain design. Despite their application in various railway vehicle problems, non-smooth models have not been explored as an alternative for analyzing stick-slip, and existing research has focused on extensive computations based on Kalker’s theory or simplified models using constitutive friction laws. This work demonstrates the efficacy of non-smooth models in studying motor wheelset stick-slip. The non-smooth approach is suited for control systems, prioritizes simplicity while capturing the essential friction characteristics, and enables efficient dynamic simulations. The proposed model incorporates a set-valued friction law, and the equations of motion are formulated as a switch model. Numerical integration is achieved through an event-driven algorithm. The paper showcases application examples for the model. A direct comparison with an equivalent model using a constitutive friction law shows that the non-smooth integration is an order of magnitude more efficient in the stick phase. Full article

The purpose of this paper is to consider a transmission problem of a viscoelastic wave with nonlocal boundary control. It should be noted that the present paper is based on the previous C. G. Gal and M. Warma works, together with H. Atoui and A. Benaissa. Namely, they focused on a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with an emphasis on rough interfaces and nonlinear dynamic (possibly, nonlocal) boundary conditions along the interface, where a transmission problem in the presence of a boundary control condition of a nonlocal type was investigated in these papers. Owing to the semigroup theory, we prove the question of well-posedness. For the very rare cases, we combined between the frequency domain approach and the Borichev–Tomilov theorem to establish strong stability results. Full article

The finite-time turnpike property describes the situation in an optimal control problem where an optimal trajectory reaches the desired state before the end of the time interval and remains there. We consider a machine learning problem with a neural ordinary differential equation that can be seen as a homogenization of a deep ResNet. We show that with the appropriate scaling of the quadratic control cost and the non-smooth tracking term, the optimal control problem has the finite-time turnpike property; that is, the desired state is reached within the time interval and the optimal state remains there until the terminal time T. The time $t_0$ where the optimal trajectories reach the desired state can serve as an additional design parameter. Since ResNets can be viewed as discretizations of neural odes, the choice of $t_0$ corresponds to the choice of the number of layers; that is, the depth of the neural network. The choice of $t_0$ allows us to achieve a compromise between the depth of the network and the size of the optimal system parameters, which we hope will be useful to determine the optimal depths for neural network architectures in the future. Full article

This paper discusses impulsive effects on fractional differential equations. Two approaches are taken to obtain our results: either with fixed or changing lower limits in Caputo fractional derivatives. First, we derive an existence result for periodic solutions of fractional differential equations with periodically changing lower limits. Then, the impulsive effects are modeled for fractional differential equations regarding the nonlinearities rather than the initial value conditions. The proposed impulsive model differs from common discontinuous and nonsmooth dynamical systems. Full article

A fully discrete scheme is proposed for numerically solving the strongly nonlinear time-fractional parabolic problems. Time discretization is achieved by using the Grünwald–Letnikov (G–L) method and some linearized techniques, and spatial discretization is achieved by using the standard second-order central difference scheme. Through a Grönwall-type inequality and some complementary discrete kernels, the optimal time-stepping error estimates of the proposed scheme are obtained. Finally, several numerical examples are given to confirm the theoretical results. Full article

Soil adhesion is one of the important factors affecting the working stability and quality of agricultural machinery. The application of bionic non-smooth surfaces provides a novel idea for soil anti-adhesion. The parameters of sandy loam with 21% moisture content were calibrated by the Engineering Discrete Element Method (EDEM). The final simulated soil repose angle was highly consistent with the measured soil repose angle, and the obtained regression equation of the soil repose angle provides a numerical reference for the parameter calibration of different soils. By simulating the sinusoidal swing of a sandfish, it was found that the contact interface shows the phenomenon of stress concentration and periodic change, which reflects the effectiveness of flexible desorption and soil anti-adhesion. The moving resistance of the wedge with different wedge angles and different serrated structures was simulated. Finally, it was found that a 40° wedge with a high-tail sparse staggered serrated structure on the surface has the best drag reduction effect, and the drag reduction is about 10.73%. Full article

The population balance equations (PBEs) serve as the primary governing equations for simulating the crystallization process. Two-dimensional (2D) PBEs pertain to crystals that exhibit anisotropic growth, which is characterized by changes in two internal coordinates. Because PBEs are the hyperbolic equations, it becomes imperative to establish a high-resolution scheme to reduce numerical diffusion and numerical dispersion, thereby ensuring accurate crystal size distribution. This paper uses Euler’s first-order explicit (EE) method–Peridynamic Differential Operator (PDDO) to solve 2D PBE, namely, the EE method for discretizing the time derivative and the PDDO for discretizing the internal crystal-size derivative. Five examples, including size-independent growth with smooth and non-smooth distributions, size-dependent growth, nucleation, and size-independent/dependent growth for batch crystallization are considered. The results show that the EE–PDDO method is more accurate than the HR method and that it is as good as the fifth-order Weighted Essential Non-Oscillatory (WENO) method in solving 2D PBE. This study extends the EE–PDDO method to the simulation of 2D PBE, and the advantages of the EE-PDDO method in dealing with discontinuous and sharp front problems are demonstrated. Full article

As a model that possesses both the potentialities of Caputo time fractional diffusion equation (Caputo-TFDE) and symmetric two-sided space fractional diffusion equation (Riesz-SFDE), time-space fractional diffusion equation (TSFDE) is widely applied in scientific and engineering fields to model anomalous diffusion phenomena including subdiffusion and superdiffusion. Due to the fact that fractional operators act on both temporal and spatial derivative terms in TSFDE, efficient solving for TSFDE is important, where the key is solving the corresponding discrete system efficiently. In this paper, we derive a Galerkin–Legendre spectral all-at-once system from the TSFDE, and then we develop a preconditioner to solve this system. Symmetry property of the coefficient matrix in this all-at-once system is destroyed so that the deduced all-at-once system is more convenient for parallel computing than the traditional timing-step scheme, and the proposed preconditioner can efficiently solve the corresponding all-at-once system from TSFDE with nonsmooth solution. Moreover, some relevant theoretical analyses are provided, and several numerical results are presented to show competitiveness of the proposed method. Full article

In this paper, we concentrate on an abstract iterative procedure for solving nonsmooth constrained generalized equations. This procedure employs both the property of weak point-based approximation and the approach of searching for a feasible inexact projection on the constrained set. Utilizing the contraction mapping principle, we establish higher order local convergence of the proposed method under the assumption of metric regularity property which ensures that the iterative procedure generates a sequence converging to a solution of the constrained generalized equation. Under strong metric regularity assumptions, we obtain that each sequence generated by this procedure converges to a solution. Furthermore, a restricted version of the proposed method is considered, for which we establish the desired convergence for each iterative sequence without a strong metric subregularity condition. The obtained results are new even for generalized equations without a constraint set. Full article