Search Results (17)

Multi-omnidirectional mobile robot formations offer significant advantages for applications in unstructured environments. However, under constraints such as limited field of view and high operator cognitive load, existing teleoperation frameworks struggle to guarantee formation safety and stability. In this study, a bilateral shared control framework for multi-robot formation that integrates intent perception and vortex-field modulation is proposed. First, an Intent-Mediated Asymmetric Vortex Modulation (IM-AVM) strategy is developed, where the operator’s micro-intentions are mapped to determine the topological orientation of a vortex field. By constructing a dynamic asymmetric modulation matrix, saddle points in the potential field are geometrically eliminated, enabling deadlock-free obstacle avoidance while maintaining a rigid formation. Second, a multi-dimensional perception-based dynamic authority arbitration and topological deadlock escape mechanism is constructed, facilitating a seamless transition from assisted deadlock to autonomous escape. Finally, a formation coordination system based on anisotropic flow field modulation and adaptive sliding mode control is designed. Rigid formation constraints are transformed into a tangential safe flow field, and robust tracking is subsequently achieved through an Adaptive Nonsingular Fast Terminal Sliding Mode Controller (ANFTSMC). Theoretical analysis and experimental results demonstrate that the proposed framework achieves collision-free navigation for the formation in simulated environments. Full article

This paper presents a preconditioner-based parallel-in-time (PinT) method for solving the quasi-static Biot’s consolidation model in poroelasticity, a problem characterized by stiff coupling and saddle-point structures. To address the computational challenges of the resulting large-scale linear systems, we design two physics-based Schur-complement approximation preconditioners that ensure robust Krylov convergence. Crucially, the method achieves a pipelined space-time architecture by introducing an inverted time-stepping mechanism: Instead of sequential time marching, time steps are traversed in the inner loop, while the outer loop applies an iterative solve across the entire space-time trajectory. This structure relaxes the strict dependency on fully converged solutions at each time step, enabling approximate solutions to be iteratively refined in parallel. Implemented as a pipelined wavefront scheme with strictly nearest-neighbor communication, the algorithm achieves strong scalability. Algorithmic verification conducted on systems with up to 200 thousand degrees of freedom demonstrates stable convergence and sustained strong scaling with up to 128 cores. The proposed approach maintains the accuracy of the underlying finite element discretization while alleviating the “time bottleneck,” making it highly effective for large-scale, long-duration poroelastic simulations. Full article

Vibration is a critical issue in aerospace structures, where lightweight design, high flexibility, and complex operational environments often lead to pronounced nonlinear dynamic responses. Excessive vibrations induced by harmonic excitations, aerodynamic loads, or onboard equipment can significantly degrade structural integrity, control accuracy, and service life. Consequently, advanced passive vibration suppression techniques with strong robustness and broadband effectiveness are of great importance in aerospace engineering applications. The bifurcation boundary and vibration suppression performance of Piezoelectric–Monostable Nonlinear Energy Sink (PMNES) are crucial for evaluating its effectiveness on the main structure. To simplify the analysis of flexible aerospace structures, a reduced-order model is derived by modal truncation in the low-frequency range, which is then treated as a two-degree-of-freedom main structure. To focus on the underlying nonlinear dynamic mechanisms, an equivalent two-degree-of-freedom lumped-parameter system is adopted as a generic representation of the dominant low-frequency dynamics of flexible aerospace structures. In this work, the electromechanical coupling control equations of the system of a two-degree-of-freedom main structure coupled with PNES are derived through the application of Newton’s second law and Kirchhoff’s voltage law. The methods of complexification-averaging (CX-A) and Runge–Kutta (RK) are employed to assess the vibration suppression performance and stability characteristics of the system under harmonic excitation. The approximate solution is validated through numerical solutions. The approximate solutions of the system are employed to derive the Saddle Node (SN) bifurcation and codimension-two cusp bifurcation points, while the enhanced algorithm is employed to ascertain the most unfavorable amplitude at each external excitation circular frequency and to determine whether the mark represents a Hopf Bifurcation (HB) point. The generalized transmissibility is utilized to assess the efficacy of vibration suppression. The various vibration suppression efficiency regions are created by superimposing the vibration suppression efficiency maps and bifurcation maps. The influence of PNES parameters on the vibration suppression region is investigated. The results indicate that this method can effectively evaluate the bifurcation boundary and vibration suppression performance of PMNES. Full article

A Multi-Layer Perceptron (MLP), as the basic structure of neural networks, is an important component of various deep learning models such as CNNs, RNNs, and Transformers. Nevertheless, MLP training faces significant challenges, with a large number of saddle points and local minima in its non-convex optimization space, which can easily lead to gradient vanishing and premature convergence. Compared with traditional heuristic algorithms relying on a population-based parallel search, such as GA, GWO, DE, etc., the Besiege and Conquer Algorithm (BCA) employs a one-spot update strategy that provides a certain level of global optimization capability but exhibits clear limitations in search flexibility. Specifically, it lacks fast detection, fast adaptation, and fast convergence. First, the fixed sinusoidal amplitude limits the accuracy of fast detection in complex regions. Second, the combination of a random location and fixed perturbation range limits the fast adaptation of global convergence. Finally, the lack of a hierarchical adjustment under a single parameter (BCB) hinders the dynamic transition from exploration to exploitation, resulting in slow convergence. To address these limitations, this paper proposes a Flexible Besiege and Conquer Algorithm (FBCA), which improves search flexibility and convergence capability through three new mechanisms: (1) the sine-guided soft asymmetric Gaussian perturbation mechanism enhances local micro-exploration, thereby achieving a fast detection response near the global optimum; (2) the exponentially modulated spiral perturbation mechanism adopts an exponential spiral factor for fast adaptation of global convergence; and (3) the nonlinear cognitive coefficient-driven velocity update mechanism improves the convergence performance, realizing a more balanced exploration–exploitation process. In the IEEE CEC 2017 benchmark function test, FBCA ranked first in the comprehensive comparison with 12 state-of-the-art algorithms, with a win rate of 62% over BCA in 100-dimensional problems. It also achieved the best performance in six MLP optimization problems, showing excellent convergence accuracy and robustness, proving its excellent global optimization ability in complex nonlinear MLP optimization training. It demonstrates its application value and potential in optimizing neural networks and deep learning models. Full article

Accurately identifying coherent vortex structures (CVSs) in backward-facing step (BFS) flows remains a challenge, particularly in reconciling visual streamlines with mathematical criteria. In this study, high-resolution velocity fields were captured using particle image velocimetry (PIV) in a pressurized BFS setup. Instantaneous streamlines reveal distinct spiral patterns, vortex centers, and saddle points, consistent with physical definitions of vortices and offering intuitive guidance for CVS detection. However, conventional vortex identification methods often fail to reproduce these visual features. To address this, an improved Q-criterion method is proposed, based on the normalization of the velocity gradient tensor. This approach enhances the rotational contribution while suppressing shear effects, leading to improved agreement in vortex position and shape with those observed in streamlines. While the normalization process alters the representation of physical vortex strength, the method bridges qualitative visualization and quantitative analysis. This streamline-consistent identification framework facilitates robust CVS detection in separated flows and supports further investigations in vortex dynamics and turbulence control. Full article

While first-order methods are popular for solving optimization problems arising in deep learning, they come with some acute deficiencies. To overcome these shortcomings, there has been recent interest in introducing second-order information through quasi-Newton methods that are able to construct Hessian approximations using only gradient information. In this work, we study the performance of stochastic quasi-Newton algorithms for training deep neural networks. We consider two well-known quasi-Newton updates, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) and the symmetric rank one (SR1). This study fills a gap concerning the real performance of both updates in the minibatch setting and analyzes whether more efficient training can be obtained when using the more robust BFGS update or the cheaper SR1 formula, which—allowing for indefinite Hessian approximations—can potentially help to better navigate the pathological saddle points present in the non-convex loss functions found in deep learning. We present and discuss the results of an extensive experimental study that includes many aspects affecting performance, like batch normalization, the network architecture, the limited memory parameter or the batch size. Our results show that stochastic quasi-Newton algorithms are efficient and, in some instances, able to outperform the well-known first-order Adam optimizer, run with the optimal combination of its numerous hyperparameters, and the stochastic second-order trust-region STORM algorithm. Full article

From the previous work, when solving the LQ optimal control problem with random coefficients (SLQ, for short), it is remarkably shown that the solution of the backward stochastic Riccati equations is not regular enough to guarantee the robustness of the feedback control. As a generalization of SLQ, interesting questions are, “how about the situation in the differential game?”, “will the same phenomenon appear in SLQ?”. This paper will provide the answers. In this paper, we consider a closed-loop two-person zero-sum LQ stochastic differential game with random coefficients (SDG, for short) and generalize the results of Lü–Wang–Zhang into the stochastic differential game case. Under some regularity assumptions, we establish the equivalence between the existence of the robust optimal feedback control strategy operators and the solvability of the corresponding backward stochastic Riccati equations, which leads to the existence of the closed-loop saddle points. On the other hand, the problem is not closed-loop solvable if the solution of the corresponding backward stochastic Riccati equations does not have the needed regularity. Full article

This paper is devoted to the investigation of optimality conditions and saddle point theorems for robust approximate quasi-weak efficient solutions for a nonsmooth uncertain multiobjective fractional semi-infinite optimization problem (NUMFP). Firstly, a necessary optimality condition is established by using the properties of the Gerstewitz’s function. Furthermore, a kind of approximate pseudo/quasi-convex function is defined for the problem (NUMFP), and under its assumption, a sufficient optimality condition is obtained. Finally, we introduce the notion of a robust approximate quasi-weak saddle point to the problem (NUMFP) and prove corresponding saddle point theorems. Full article

In some statistical methods, the statistical information is provided in terms of the values used by classical estimators, such as the sample mean and sample variance. These estimations are used in a second stage, usually in a classical manner, to be combined into a single value, as a weighted mean. Moreover, in many applied studies, the results are given in these terms, i.e., as summary data. In all of these cases, the individual observations are unknown; therefore, computing the usual robustness estimators with them to replace classical non-robust estimations by robust ones is not possible. In this paper, the use of the median of the distribution $F_{\overline{x}}$ of the sample mean is proposed, assuming a location-scale contaminated normal model, where the parameters of $F_{\overline{x}}$ are estimated with the classical estimations provided in the first stage. The estimator so defined is called median of the distribution of the mean, $MdM$. This new estimator is applied in Mendelian randomization, defining the new robust inverse weighted estimator, RIVW. Full article

For system identification under impulsive-noise environments, the gradient-based generalized maximum correntropy criterion (GB-GMCC) algorithm can achieve a desirable filtering performance. However, the gradient method only uses the information of the first-order derivative, and the corresponding stagnation point of the method can be a maximum point, a minimum point or a saddle point, and thus the gradient method may not always be a good selection. Furthermore, GB-GMCC merely uses the current input signal to update the weight vector; facing the highly correlated input signal, the convergence rate of GB-GMCC will be dramatically damaged. To overcome these problems, based on the Newton recursion method and the data-reusing method, this paper proposes a robust adaptive filtering algorithm, which is called the Newton recursion-based data-reusing GMCC (NR-DR-GMCC). On the one hand, based on the Newton recursion method, NR-DR-GMCC can use the information of the second-order derivative to update the weight vector. On the other hand, by using the data-reusing method, our proposal uses the information of the latest M input vectors to improve the convergence performance of GB-GMCC. In addition, to further enhance the filtering performance of NR-DR-GMCC, a random strategy can be used to extract more information from the past M input vectors, and thus we obtain an enhanced NR-DR-GMCC algorithm, which is called the Newton recursion-based random data-reusing GMCC (NR-RDR-GMCC) algorithm. Compared with existing algorithms, simulation results under system identification and acoustic echo cancellation are conducted and validate that NR-RDR-GMCC can provide a better filtering performance in terms of filtering accuracy and convergence rate. Full article

Federated learning (FL) is a distributed neural network training paradigm with privacy protection. With the premise of ensuring that local data isn’t leaked, multi-device cooperation trains the model and improves its normalization. Unlike centralized training, FL is susceptible to heterogeneous data, biased gradient estimations hinder convergence of the global model, and traditional sampling techniques cannot apply FL due to privacy constraints. Therefore, this paper proposes a novel FL framework, federated lazy aggregation (FedLA), which reduces aggregation frequency to obtain high-quality gradients and improve robustness in non-IID. To judge the aggregating timings, the change rate of the models’ weight divergence (WDR) is introduced to FL. Furthermore, the collected gradients also facilitate FL walking out of the saddle point without extra communications. The cross-device momentum (CDM) mechanism could significantly improve the upper limit performance of the global model in non-IID. We evaluate the performance of several popular algorithms, including FedLA and FedLA with momentum (FedLAM). The results show that FedLAM achieves the best performance in most scenarios and the performance of the global model can also be improved in IID scenarios. Full article

The spatio-temporal variogram is an important factor in spatio-temporal prediction through kriging, especially in fields such as environmental sustainability or climate change, where spatio-temporal data analysis is based on this concept. However, the traditional spatio-temporal variogram estimator, which is commonly employed for these purposes, is extremely sensitive to outliers. We approach this problem in two ways in the paper. First, new robust spatio-temporal variogram estimators are introduced, which are defined as M-estimators of an original data transformation. Second, we compare the classical estimate against a robust one, identifying spatio-temporal outliers in this way. To accomplish this, we use a multivariate scale-contaminated normal model to produce reliable approximations for the sample distribution of these new estimators. In addition, we define and study a new class of M-estimators in this paper, including real-world applications, in order to determine whether there are any significant differences in the spatio-temporal variogram between two temporal lags and, if so, whether we can reduce the number of lags considered in the spatio-temporal analysis. Full article

This paper focuses on robustness and sensitivity analysis for sensor fault diagnosis of a voltage source converter based microgrid model. It uses robust control parameters such as minimum sensitivity parameter $(H-)$, maximum robustness parameter $(H\infty )$, and compromised both $(H-/H\infty )$, being incorporated in the sliding mode observer theory using the game theoretic saddle point estimation achieved through convex optimization of constrained LMIs. The approach used works in a way that the mentioned robust control parameters are embedded in Hamilton–Jacobi–Isaacs-Equation (HJIE) and are also used to determine the inequality version of HJIE, which is, in terms of the Lyapunov function, faults/disturbances and augmented state/output estimation error as its variables. The stability analysis is also presented by negative definiteness of the same inequality version of HJIE, and additionally, it also gives linear matrix inequalities (LMIs), which are optimized using iterative convex optimization algorithms to give optimal sliding mode observer gains enhanced with robustness to maximal preset values of disturbances and sensitivity to minimal preset values of faults. The enhanced sliding mode observer is used to estimate states, faults, and disturbances using sliding mode observer theory. The optimality of sliding mode observer gains for sensitivity of the observer to minimal faults and robustness to maximal disturbance is a game theoretic saddle point estimation achieved through convex optimization of LMIs. The paper includes results for state estimation errors, faults’ estimation/reconstruction, fault estimation errors, and fault-tolerant-control performance for current and potential transformer faults. The considered faults and disturbances in current and potential transformers are sinusoidal nature composite of magnitude/phase/harmonics at the same time. Full article

In this paper, we introduce a new class of multi-dimensional robust optimization problems (named $(P)$) with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Moreover, we define an auxiliary (modified) class of robust control problems (named ${(P)}_{(\overline{b},\overline{c})}$), which is much easier to study, and provide some characterization results of $(P)$ and ${(P)}_{(\overline{b},\overline{c})}$ by using the notions of normal weak robust optimal solution and robust saddle-point associated with a Lagrange functional corresponding to ${(P)}_{(\overline{b},\overline{c})}$. For this aim, we consider path-independent curvilinear integral cost functionals and the notion of convexity associated with a curvilinear integral functional generated by a controlled closed (complete integrable) Lagrange 1-form. Full article

Let $\mathbf{Z}(\mathbf{s})={(Z_1(\mathbf{s}),\dots ,Z_p(\mathbf{s}))}^t$ be an isotropic second-order stationary multivariate spatial process. We measure the statistical association between the p random components of $\mathbf{Z}$ with the correlation coefficients and measure the spatial dependence with variograms. If two of the $\mathbf{Z}$ components are correlated, the spatial information provided by one of them can improve the information of the other. To capture this association, both within components of $\mathbf{Z}(\mathbf{s})$ and across $\mathbf{s}$, we use a cross-variogram. Only two robust cross-variogram estimators have been proposed in the literature, both by Lark, and their sample distributions were not obtained. In this paper, we propose new robust cross-variogram estimators, following the location estimation method instead of the scale estimation one considered by Lark, thus extending the results obtained by García-Pérez to the multivariate case. We also obtain accurate approximations for their sample distributions using saddlepoint techniques and assuming a multivariate-scale contaminated normal model. The question of the independence of the transformed variables to avoid the usual dependence of spatial observations is also considered in the paper, linking it with the acceptance of linear variograms and cross-variograms. Full article