This study addresses the stabilization challenge in linear Itô stochastic systems subject to noisy sampling intervals. First, the linear Itô stochastic system is converted into an equivalent discrete-time system via the lifting technique. Then, the expected value of the quadratic form of the state transition matrix is simplified by using the related properties of the Wiener process and matrix exponential function, thereby decoupling the dual randomness arising from the system stochasticity and the noisy sampling intervals. Subsequently, by introducing the Kronecker product and confluent Vandermonde matrix, the expected value of a product of multiple matrices is calculated. Based on the theoretical framework, the stabilization controller is developed to ensure stochastic stability of the resulting closed-loop system. Finally, a numerical example is given to demonstrate the efficacy of the proposed control strategy.

In this paper, we investigate the problem of impulsive synchronization in third-order nonlinear multi-agent systems under the influence of Denial-of-Service (DoS) attacks. The study focuses on scenarios where DoS nodes intermittently disrupt communication links, restricting information flow and dynamically altering the network topology. To address these challenges, we propose an impulsive, event-triggered control strategy that efficiently balances communication constraints with system performance. The designed controller explicitly accounts for external disturbances and actuator limitations through input saturation constraints, ensuring that control inputs remain within feasible bounds. By integrating event-triggering mechanisms with impulsive control actions, the approach minimizes unnecessary control updates while maintaining robust synchronization across the network. Furthermore, the method includes safeguards to preserve stability under bounded DoS attack durations, ensuring that the system maintains consistent behavior even during communication interruptions. Importantly, the proposed framework is applicable to both directed and undirected network topologies, guaranteeing reliable consensus irrespective of the underlying graph structure. To validate the effectiveness and practical utility of the strategy, comprehensive numerical simulations are presented, demonstrating the controller’s ability to achieve high-precision synchronization while mitigating the adverse effects of DoS attacks and disturbances.

This paper studies delay-dependent consensus in distributed multi-agent systems with linear agent dynamics under a memory-type current-minus-delayed relative-state diffusive interaction. In this protocol, the parameter $\tau$ is a common memory interval for stored relative-state measurements, and the feedback term vanishes when $\tau=0$. By exploiting the spectral decomposition of an undirected communication graph, the memory-coupled network is transformed into independent modal subsystems, each described by a linear retarded differential equation. For these modes, structured Lyapunov-Krasovskii functionals with matrix decision variables are constructed, leading to delay-dependent stability conditions in the form of linear matrix inequalities (LMIs). The resulting mode-wise LMIs explicitly depend on the subsystem matrices, feedback gain, Laplacian eigenvalues, and the memory interval, thereby providing sufficient stability certificates for prescribed positive values of $\tau$. A structural implication of the proposed LMI condition is that the intrinsic agent matrix $A$ is Hurwitz; accordingly, the LMI certificate gives a state-space memory-robustness test for Hurwitz linear agents. The numerical section combines a frequency-domain modal root-crossing illustration for a harmonic-oscillator network with an LMI-certified computation for a Hurwitz-agent network.

We study partial differential resultants for systems of n + 1 generic partial differential polynomials in n differential indeterminates. Although the associated coefficient elimination ideal is prime of codimension one, unlike in the algebraic and ordinary differential cases, it need not be the general component of a single irreducible differential polynomial. We define the partial differential resultant precisely when such a principal representation exists. For two generic univariate differential polynomials, we prove that the partial differential resultant exists if and only if at most one polynomial has positive order. In the multivariate case, we show that having at most one positive-order polynomial is sufficient for existence, whereas the partial differential resultant does not exist when exactly two polynomials have positive order. We conjecture that this condition is also necessary. We further establish fundamental properties of partial differential resultants and introduce sparse partial differential resultants for two univariate sparse partial differential polynomials containing degree-zero terms. These results clarify the structural boundary for the existence of partial differential resultants and lay a foundation for further developments in the theory of partial differential resultants.

This paper surveys the development of control and stabilization theory for nonlinear dispersive wave equations on periodic domains, with particular emphasis on the role of harmonic analysis. The principal focus is the Korteweg-de Vries (KdV) equation, the first nonlinear dispersive model to be systematically investigated from a control-theoretic perspective. We review the resolution of fundamental questions concerning exact controllability and exponential stabilization on the torus T, achieved through the interplay between Bourgain-type spaces and control-theoretic methods, in both local and global settings. We also discuss extensions to coupled KdV-KdV systems, including the resolution of the previously open question of whether such systems are locally exactly controllable and locally exponentially stabilizable. The aim is to provide a unified account of these developments and to highlight the deep connections between low-regularity well-posedness and control theory, as well as the central role played by harmonic analysis in this context.

This paper presents a port-Hamiltonian (PH) modeling, control, and structure-preserving simulation framework for grid-forming static var generators (SVGs). A PH model is established that captures energy exchange among the inductor, capacitor, and DC-link storage ports. Since external disturbances cannot be fully canceled by feedback, an input-to-state stable (ISS) controller is designed to steer subsystem states to zero while minimizing disturbance effects. The controller contains only three tunable parameters with clear physical interpretations and is robust against input errors. A Dirac-structure-preserving midpoint rule is developed, which exactly conserves the Hamiltonian energy when disturbances are absent. Numerical comparisons show that the ISS controller achieves faster settling, smaller offset, and lower control effort than a conventional PI controller, and the structurepreserving midpoint rule maintains exact energy conservation and superior long-term accuracy over standard Runge-Kutta methods.

A recursive approach is developed to characterize the variance of gene expression. The approach decomposes a complex problem into a sequence of simple recursive steps, with the key advantage of being readily extensible to large gene regulatory networks. In this paper, we apply the approach to an arbitrarily large cascade of regulated genes, while it can also be extended to networks with more general structures. The resulting formulas provide a quantitative means of understanding the accumulation and suppression of noise in gene regulatory networks.

This paper investigates the distributed consensus control problem for a class of high-order nonlinear multi-agent systems (MASs) subject to actuator dead-zone nonlinearities and severely constrained communication resources. To simultaneously guarantee rigorous control performance and improve bandwidth efficiency, we propose a novel framework integrating a 4-level quantized event-triggered mechanism (ETM) with an adaptive prescribed performance controller (PPC). Unlike conventional ETMs that transmit full-precision continuous signals, the proposed quantized ETM discretizes the control execution signals into four distinct levels, requiring only a 2-bit data packet per transmission. This significantly compresses the data payload while reducing the transmission frequency. Developed via Lyapunov stability theory and backstepping design, the proposed control strategy ensures that all closed-loop signals are uniformly ultimately bounded and that consensus tracking errors strictly evolve within the predefined performance envelopes, despite the quantization errors introduced by the ETM. Simulation results demonstrate that the proposed method reduces the triggering frequency by 88.65% compared to time-triggered mechanisms, validating its enhanced bandwidth efficiency and robustness.

This paper is devoted to stochastic approximation with mean-field interactions. First, stochastic approximation with mean-field interactions is presented. The algorithms are given. Then the asymptotic analysis is provided. Finally, some remarks are provided.

We study consensus behavior for both standard and leadership-based Hegselmann-Krause models with transmission delay on countably infinite weighted graphs. Our analysis avoids Lyapunov methods and instead studies the contraction of the opinion diameter within a deterministic iterative framework, yielding quantitative finite-time contraction estimates and asymptotic consensus through iteration. Furthermore, we present a phased admissible control strategy within the leadership framework that addresses the bounded-confidence restriction on follower interactions. We establish global well-posedness, prove asymptotic consensus for arbitrary transmission delay under a suitable boundarylayer mass condition, and show that finitely many leaders can asymptotically steer a countably infinite weighted follower system to any prescribed target opinion.

In this paper, we investigate aperiodic model predictive control (MPC) strategies for load frequency control (LFC) of power systems with wind power integration. An adaptive event-triggered MPC that incorporates a dynamic triggering threshold and a decreasing prediction horizon to actively regulate the optimization frequency based on real-time frequency deviations is designed. To avoid the continuous state monitoring required by the event-triggered mechanism, an adaptive self-triggered MPC that proactively computes the subsequent execution instant using the current state and control information is proposed. By implementing these triggered paradigms, the proposed methods significantly reduce the computational complexity and triggering frequency, thereby reducing communication and computational burdens. Finally, simulation results are presented to verify the effectiveness and advantages of the proposed control strategies.

This paper targets at developing efficient data-based iterative learning control approaches by utilizing prior knowledge related to Markov parameter matrix. For both square and non-square systems, experiment design methods are proposed to collect data along the iteration axis, and necessary and sufficient conditions are developed under which the collected data are informative for output tracking. Through exploiting the informative data and incorporating the prior knowledge, iterative learning controllers are synthesized for both square and non-square systems. It is shown that, by leveraging the prior knowledge associated with Markov parameter matrix, the proposed approaches can achieve point-to-point output tracking with a relatively small amount of data and a finite number of iterations. The effectiveness of the proposed approaches is demonstrated through simulations on mobile robots and permanent magnet synchronous motors.

In imperfect-information extensive-form games (EFGs), full feedback is often impractical: real platforms reveal only trajectory outcomes due to privacy, partial observability, and the cost of fulltree traversals. This necessitates bandit feedback, which is scalable but yields high-variance signals. However, under bandit feedback, many existing methods only guarantee average-iterate convergence, limiting their practicality for deployment. This paper addresses the problem of finding an approximate Nash equilibrium (NE) in EFGs under bandit feedback. We propose Variance-Reduced Perturbed Optimistic Online Mirror Descent (VR-POOMD), which integrates a perturbed strategy for regularization and an unbiased variance-reduced gradient estimator. First, we introduce a regularized formulation whose unique Nash equilibrium z^*_β is an approximate Nash equilibrium of the original game, with the approximation error controlled by the regularization coefficient β and the perturbed strategy. Second, we design an unbiased variance-reduced gradient estimator that uses players’ observations by sampling with depth-weighted, action-count-aware probabilities and leveraging a periodically updated reference strategy to shrink variance over time. For a fixed perturbed strategy, we prove that VR-POOMD achieves almost-sure last-iterate convergence to the unique regularized equilibrium, with an expected O(1/t) convergence rate in Bregman divergence. Numerical simulations validate the effectiveness of the proposed method.

The deployment of control systems with network-connected sensors makes them vulnerable to sensor-network attacks. This paper studies robust prognosability of sensor-compromised discrete event systems, where an attacker can erase or insert vulnerable sensor readings. Prognosability requires that any critical event of interest be predicted before its occurrence, but this property may be destroyed by manipulated observations. We first construct a new verifier that explicitly incorporates the attacker's stealthiness to assess robust prognosability (RP) under sensor attacks. When RP is violated, we further examine the existence of a successful attacker (RA), namely one that destroys prognosability while remaining stealthy.We develop an insertion-erasure attack (IEA) structure that exactly characterizes whether such an attacker exists. Finally, the theoretical results are validated in the transportation domain through a high-speed railway traction power supply protection system.

This study introduces a model-free deep reinforcement learning (DRL) framework to address mean-variance portfolio optimization for logarithmic returns in the presence of transaction costs. Unlike conventional approaches that typically model transaction costs using simplified $L_1$ or $L_2$ penalties, our method explicitly incorporates asymmetric costs for buying and selling, alongside fixed transaction costs, to better capture market frictions. These costs introduce non-convex, non-linear, and non-smooth optimization challenges that traditional stochastic control and numerical methods struggle to address. To overcome these limitations, we develop a DRL framework based on the deterministic policy gradient method, with tailored gradient formulations to ensure computational efficiency. Numerical analysis demonstrates that strategies optimized without considering transaction costs exhibit unstable performance in frictional markets, highlighting the critical need for accurate cost modeling. Furthermore, the proposed framework exhibits strong generalizability, accommodating short-selling constraints, standard mean-variance optimization and extensions to semivariance formulations, while maintaining robust performance across diverse financial scenarios.

This paper investigates opinion evolution within social networks, focusing on the role of bounded confidence in social cliques. We first propose a framework where agents' initial opinions are independently and identically distributed. At each time step, agents assess the average opinion of a randomly selected local clique, which represents local group pressure. Subsequently, agents update their opinions using the DeGroot rule subject to bounded confidence; specifically, an update occurs only if the divergence between an agent's opinion and the local clique pressure falls below a specified threshold. This framework generalizes the classical Deffuant-Weisbuch pairwise interaction model. We demonstrate that, under specific initial and parameter conditions, opinion fluctuations occur with strictly positive probability. Furthermore, we identify a specific initial value event under which fluctuation arises with probability one. These results deepen the understanding of bounded confidence mechanisms and reveal that the inclusion of clique dynamics fundamentally alters the behavior of the Deffuant-Weisbuch model by introducing the possibility of persistent fluctuation.

This paper proposes a new nonparametric forecasting procedure based on a weighted local linear estimator for a nonparametric model with structural breaks. The proposed method assigns weights based on both the distance of observations to the predictor covariates and their temporal position with respect to structural breaks (i.e., pre-break versus post-break). These weights are chosen using multifold forward-validation to account for time series data. We investigate the asymptotic properties of the proposed estimator and show that the weight estimated by the multifold forward-validation is asymptotically optimal in the sense of achieving the lowest possible out-of-sample prediction risk. Additionally, a nonparametric method is adopted to estimate the break date, and the proposed approach allows for different features of predictors before and after break. A Monte Carlo simulation study is conducted to provide evidence for the forecasting outperformance of the proposed method over the regular nonparametric post-break and full-sample estimators. Finally, an empirical application to inflation forecasting compares several popular parametric and nonparametric methods, including the proposed weighted local linear estimator.

Inverse optimal control (IOC) provides a principled way to model an expert's decision mechanism from its demonstrations. In particular, it seeks a structured cost function that rationalizes the expert's observed state-action trajectories. This paper studies the problem of IOC for discrete-time nonlinear stochastic systems under the long-run average-cost criterion. More specifically, the expert is modeled by a stationary deterministic policy that is optimal for a Markov control model with a known transition kernel and an unknown stage cost, where the stage cost is a linear combination of known feature functions. We first rewrite the forward average-cost problem as an invariant occupation-measure linear program and use its dual Bellman inequality to characterize optimality through a nonnegative Bellman residual. Based on this optimality condition, we construct a convex inverse problem that builds on the invariant occupation measure and searches for a candidate cost parameter and a relative value function that rationalize the demonstrations. Since the invariant occupation measure is not directly observable from finite demonstrations, we replace it by a finite-horizon occupation measure and then by its empirical approximation, leading to a polynomial semi-infinite approximation and a tractable WSOS-based numerical implementation. It is proved that the recovered cost admits an optimal policy that agrees with the demonstrated expert actions on the observed samples, and the integrated Bellman residual of the semi-infinite approximation converges to zero for fixed $N$ under the stated sequential limiting regime. The proposed algorithm is further illustrated by numerical experiments on a stochastic linear quadratic regulator and a nonlinear temperature-control system.

We derive precise asymptotic expressions for the expectations, variances, covariance, and quite a few further mixed moments for the number of hairpins and the number of basepairs in RNA secondary structures, and give convincing evidence that the central-scaled distribution of the pair of random variables (hairpins, basepairs) tends in distribution to the bi-variate normal distribution with correlation $\sqrt{5 \sqrt{5} -11}/2= 0.2123322205\dots$

This paper investigates the problem of target protection of heterogeneous nonlinear multiagent systems with conflicting goals. To characterize the competitive interactions arising from their conflicting goals, the problem is first transformed into a time-varying non-cooperative game, whose Nash equilibrium is the optimal solution to the original problem. Then, a novel distributed timevarying Nash equilibrium seeking algorithm is proposed based on a leader-following consensus protocol and sliding-mode theory. It is proved that the actions of the players under the proposed distributed algorithm converge to the Nash equilibrium in fixed time, with an explicitly given upper bound on the convergence time. The effectiveness of the proposed distributed algorithm is validated via an example involving a group of unmanned aerial vehicles.

This paper investigates the output regulation problem for a class of unknown nonlinear systems directly from noisy data. The considered systems are described by a state-dependent representation, in which the nonlinear dynamics are expressed as a linear combination of known basis functions with unknown coefficients. To circumvent the need for explicitly solving the generally intractable nonlinear output regulator equations, the internal model principle is exploited to convert the regulation problem into a stabilization problem of an augmented system embedding a k-fold internal model of the exosystem. Based on noisy input-state data collected from offline experiments, we derive a direct data-driven framework that reduces the controller synthesis problem to a data-dependent semidefinite program, with local stability and approximate regulation guarantees. In particular, the uncertainty induced by unmeasurable exosignals is handled through a suitable matrix factorization, while the effect of noisy data is addressed via Petersen’s lemma. Numerical simulations on a quadrotor attitude regulation example demonstrate the effectiveness of the proposed approach.

Large-scale ocean fields support marine environmental monitoring, climate analysis, and autonomous ocean sensing. Accurate prediction remains challenging because ocean temperature exhibits strong horizontal coherence, vertical stratification, and slow background variation. This paper proposes a graph-structured spatiotemporal method for three-dimensional ocean temperature field prediction. Each snapshot is represented as a graph signal on separate horizontal and vertical graphs, and recent field increments are propagated through local, horizontal, vertical, and mixed graph bases to construct graph-temporal features. A horizon-dependent dynamic correction is identified under graph Laplacian regularization and added to the current field to obtain the predicted full-field state. Validation-based basis selection and gain calibration adapt the graph propagation form and correction amplitude to different prediction horizons. Experiments achieve a one-step RMSE of 0.0714°C, reducing RMSE by 4.80% relative to the increment-only model and by 40.10% relative to persistence. Multistep, depth-wise, and input-perturbation analyses further demonstrate accurate and robust prediction while preserving the principal three-dimensional thermal structure.

In this article, the predefined-time distributed optimization problem is investigated for high-order nonlinear multi-agent systems (MASs) subject to unmatched disturbances and uncertain state constraints. A distributed proportional-integral (PI) protocol is first introduced to construct a reference model for estimating the global optimum. The estimated values are then processed by a prefilter to reconstruct the optimal reference signal along with its higher-order derivatives. A major challenge arises when reference trajectories violate state constraints, which complicates the controller design. To overcome this, a smooth and safety-guaranteed reference generation mechanism is developed to ensure safe tracking under conflicting state constraints. Furthermore, within the prefiltering framework, a neural network-based predefined-time control scheme is established using a prescribedtime nonlinear disturbance observer and backstepping technique, guaranteeing that all agents attain state-constrained optimal consensus within the predefined timeframe. The feasibility of the presented approach is demonstrated via simulations.

This paper investigates the trajectory tracking problem for uncertain Euler-Lagrange (EL) systems subject to disturbances and prescribed performance constraints. The proposed approach combines the robust adaptive control scheme with barrier Lyapunov function (BLF). The robust adaptive approach can handle uncertain system parameters and disturbances with unknown bounds by estimating these two bounds. By incorporating a BLF into the robust adaptive control scheme, the proposed method guarantees the satisfaction of both the transient and steady-state performance specifications without knowing the bounds of uncertain system parameters and disturbance. Lyapunov-based analysis proves that the tracking error meets the prescribed performance and that both position and velocity tracking errors converge to zero asymptotically. The effectiveness of the proposed control strategy is verified by a simulation.

This paper develops a model-informed deep learning approach for optimal pairs trading. The spread between two historically correlated securities is modeled as a mean-reverting Ornstein–Uhlenbeck process, and the trading problem incorporates fixed transaction costs and a stop-loss constraint. The associated Hamilton–Jacobi–Bellman (HJB) formulation leads to a system of quasivariational inequalities, under which the optimal trading rule is characterized by three threshold levels. The proposed neural network is trained as an amortized surrogate for this threshold map. Specifically, Monte Carlo sample paths generated from the mean-reverting model, together with path-level summary statistics, are used as inputs, while the HJB-generated thresholds serve as supervised training targets. After offline training, the learned network provides fast feed-forward predictions of threshold levels for empirical spread data after suitable preprocessing. We construct stochastic-approximation algorithms for training, establish their convergence using weak convergence methods, and present numerical experiments comparing several neural network architectures. A real-market spread-level backtesting example is also provided to illustrate the implementation of the learned-threshold strategy.

This paper will investigate the maximum capabilities of sampled-data feedback for uncertain nonlinear systems subject to linear growth constraints. For a basic class of one-dimensional uncertain nonlinear control systems, we will analyze how the sampled-data feedback stabilizability depends on both the sampling period $h$ and the linear growth constant $L$. On the impossibility side, we will prove that whenever $Lh>4.19$, no sampled-data feedback law can stabilize the entire class of systems, thereby improving the previous constant $4.75$. On the possibility side, we will prove that uniform stabilization can be guaranteed when $Lh < 2$, thus extending the previously known constant $\log 4\approx 1.386$. As a consequence, the unresolved parameter interval for feedback stablization will be reduced from $[1.38,\,4.75]$ to $[2,\,4.19]$, which clearly narrows the gap between currently known necessary and sufficient conditions and thereby provides deeper insight into the intrinsic capabilities of sampled-data feedback for nonlinear systems.

The family, as the fundamental unit of disaster management, plays a crucial role in pre-disaster prevention, mitigating the impact of disasters, and post-disaster recovery and reconstruction. Taking 13 streets and townships in Wancheng District, Nanyang City as the research objects, the fuzzy Delphi Method and the Analytic Hierarchy Process were employed. Through a questionnaire survey, the demographic characteristics of residents, their disaster perception ability, community support level, participation level, and family preparedness capacity were collected to construct a family resilience assessment framework for measuring the family resilience level. The findings reveal that the overall family resilience in Wancheng District is within the ‘low-to-moderate' range and shows a ‘rural high-urban low' trend. Among the factors, community support is identified as the most significant influence on family resilience in Wancheng District. Based on these findings, enhancing the level of family resilience to respond to natural disasters holds certain reference value for improving grassroots emergency management systems.

This paper investigates the stability and robustness of a class of recurrent neural network controllers (RNNCs) for nonlinear uncertain systems. For the cases of \(n=1\) and \(n\geq 2\), the conditions for setting the parameters of RNNCs, rather than training, to ensure the states of the closed-loop systems convergence to the target values are provided. Meanwhile, the quantitative relationships between the RNNC parameters and the range of the initial state, target value, plant uncertainty and external disturbance are presented. Moreover, a fundamental limitation for RNNCs is proved: RNNCs with bounded activation functions cannot globally stabilize even linear uncertain plants. Finally, numerical simulations are provided to verify the theoretical results.

This paper integrates the ``control design'' idea to develop some iterative methods for the solving of linear algebraic equations (LAEs), which brings a new perspective to establish the connections between mathematics and control such that the applicability of iterative methods may be improved. A control system related to the LAE is first constructed, where the output controllability and the state observability of this control system are disclosed to have the equivalent relations with the solvability and the solution uniqueness of the LAE, respectively, from a unified viewpoint. Based on these equivalent relations, an iterative method is further proposed under the error-based feedback controller by exploiting the relation for the solving problem of the LAE and the output reference tracking problem of its induced control system. As a consequence, all (least squares) solutions can be obtained in an analytical form for any (un)solvable LAE, which depends linearly on the initial condition. As an additional benefit, it is shown that the general solution and the particular (least squares) solution for any (un)solvable LAE coincide with the unobservable state and the observable state of its induced control system, respectively.

The LOL algorithm is a stream cipher with extremely high throughput, proposed by Feng et al. recently to meet the high-throughput demands of 6G communications. It contains two main variants: LOL-MINI and LOL-DOUBLE. This study focuses on the permutation property of the initialization round function $\mathcal{F}$ in LOL-MINI. Our results show that $\mathcal{F}$ is not a permutation. Specifically, we first reduce $\mathcal{F}$ to a simpler mathematical function $\mathcal{G}$, then apply differential analysis together with MILP tools to find a valid collision for $\mathcal{G}$ within minutes on a personal computer. Exploiting the relation between $\mathcal{G}$ and $\mathcal{F}$, any single collision of $\mathcal{G}$ immediately yields $2^{128}$ distinct collisions of $\mathcal{F}$. It shows that the LOL-MINI round function possesses a huge number of valid collisions. The above approach also applies to the initialization round function of LOL-DOUBLE. Despite the existence of this large class of collisions, we have not yet found a method to translate this structural property into a practical weak-key attack.

Existing research on distributed dynamic optimization typically focuses on single-objective or static scenarios and often assumes that system dynamics are negligible at the optimal solution, making it challenging to achieve an effective trade-off between multiple objectives while ensuring theoretical convergence. To address the dynamic optimization problem characterized by conflicting bi-objectives in multi-agent networks, we propose a hierarchical decoupled cooperative control framework based on virtual leaders. Unlike the limitations of existing weighted-sum methods that require globally consistent weights, or distributed evolutionary algorithms that suffer from slow convergence and lack theoretical guarantees, the proposed method delegates the multi-objective optimization task to virtual leaders for centralized processing. Consequently, agents are only required to track the states of these leaders, thereby significantly reducing computational and communication burdens. Targeting two typical scenarios where system dynamics are either zero or non-zero at the optimal solution, we design distributed controllers and an estimation-based compensation mechanism, respectively. Furthermore, explicit conditions for gain design are derived based on the Lyapunov analysis, providing a rigorous proof of the convergence of the closed-loop system. Simulation results demonstrate that the proposed method not only achieves a tunable trade-off between conflicting objectives but also effectively handles non-zero dynamic perturbations, exhibiting superior adjustability and robustness.

This paper investigates demand information sharing in agency channels across four supply chain structures defined by upstream competition (common vs. independent manufacturer) and downstream competition (monopoly vs. duopoly agent). Incorporating endogenous sales effort and heterogeneous signal accuracy, we characterize the equilibrium sharing decisions of all supply chain members and evaluate their social welfare implications. We show that information sharing is always a Pareto improvement under the Monopoly/Common structure, while the agent optimally shares with at most one manufacturer under the Monopoly/Independent structure when competition is sufficiently intense. Under the Duopoly/Common structure, asymmetric signal precision introduces endogenous free-riding incentives that may shift the equilibrium from full sharing to partial sharing, a result that cannot arise under symmetric accuracy assumptions. The Duopoly/Independent structure uniquely achieves full sharing as the dominant equilibrium, with private incentives perfectly aligned with the social optimum. A cross-structure welfare analysis further reveals that supply chain organizational form is a first-order determinant of system efficiency, while the efficiency improvement from information sharing is remarkably uniform across all structures regardless of organizational configuration. These findings provide actionable guidance for agency operators: structural configuration should precede information policy design, and targeted interventions are warranted only in structures in which private and social incentives diverge.

This paper investigates the sampled-data output-feedback group consensus problem for strict-feedback nonlinear multi-agent systems based on the gain control method. It is noteworthy that the considered system is subject to packet losses, which has not been addressed in existing studies. To address this challenge, a distributed sampled-data output-feedback control protocol is proposed. Specifically, the update of the controller relies on successful data transmission, effectively coping with the performance degradation caused by packet losses. Subsequently, by dividing the time interval into sampling intervals and packet loss intervals, as well as combining Lyapunov stability theory and Lyapunov-Krasovskii functionals, it is proved that the desired group consensus can be achieved by the proposed control protocol. Further, the results are extended to the scenario where the system simultaneously suffers from packet losses and communication delays, establishing the relationship between the packet loss rate, communication delay, sampling period, and control gain. Finally, the effectiveness of the proposed control scheme is verified through simulation examples.

This paper investigates the event-triggered consensus problem of linear multi-agent systems (MASs) under distributed denial-of-service (DDoS) attacks from multiple attackers that target different communication channels. The joint connectivity of the physical topology induced by the DDoS attacks is analyzed, which is shown to be a necessary yet insufficient condition for the joint connectivity of the communication topology induced by the interaction between DDoS attacks and event-triggered communication. To ensure the joint connectivity of the resulting communication topology, we design a dynamic secure controller with a novel consensus protocol and a novel event-triggered mechanism that includes a communication recovery detection strategy. Then, asymptotic consensus is theoretically established, with a guaranteed exclusion of Zeno behavior. Finally, the effectiveness of the proposed approach is verified through numerical simulations.

Visual localization systems rely on local image descriptors to enable pose estimation and loop closure, yet face a critical trade-off between accuracy and efficiency in resource-constrained settings. High-dimensional floating-point descriptors provide strong matching performance but impose significant communication and storage overhead, especially in distributed or embedded applications. Conversely, compact binary descriptors reduce resource demands but suffer from notable performance degradation under challenging conditions. To bridge this gap, we propose a geometry-aware selfsupervised distillation framework that converts pretrained floating-point descriptors into compact binary codes while preserving their geometric structure. Our method formulates the quantization process as a Semi-Orthogonal Procrustes Problem, ensuring that pairwise descriptor similarities are retained during binarization. A lightweight single-layer MLP is then used to perform the transformation, maintaining compatibility with existing pipelines. Experiments demonstrate that our approach preserves the accuracy of state-of-the-art floating-point descriptors while leveraging the efficiency of binary representations, establishing a new state-of-the-art for binary descriptors in visual localization systems.

This paper investigates the parameter identification problem of Takagi-Sugeno (T-S) fuzzy systems under quantized output measurements. In contrast to conventional identification theories that rely on continuous-valued observations, quantization mechanism introduces nonlinear and non-smooth error structures, which fundamentally alter the statistical properties of the identification problem and render classical analytical methods inapplicable. To address this issue, we first consider the case where the membership weights are known. By constructing a periodic structure involving the input and the membership functions, a parameter identification algorithm based on periodic excitation is developed, and the strong consistency of the parameter estimates is rigorously established. Subsequently, for the case with unknown membership weights, a set of nonlinear equations incorporating the parameters of the membership functions is formulated. The identifiability and local solvability conditions of this system are analyzed, and a data-driven approach is proposed to achieve joint identification of the local model parameters and the membership function parameters. Finally, numerical simulations are conducted to validate the effectiveness and convergence performance of the proposed methods. This work systematically reveals the underlying principles of T-S fuzzy system identification under quantized observations, and provides a generalizable theoretical foundation for the identification and analysis of nonlinear systems with finite-precision measurements.

How to derive optimal control strategies for preventing the spread of two-strain competing epidemics in complex networks is a significant challenge. This paper first establishes two-strain epidemic models with mutations and imperfect immunity in a single-layer network, which incorporate control measures in the infection compartment to find optimal control strategies. Then, the equilibrium states of the system are analyzed by classifying them into three different types, and the stability conditions are derived. Next, we design an optimal curing strategy that globally minimizes both epidemic severity and control costs in the network. Furthermore, the predictability of epidemic spread is demonstrated by establishing structural insights into its existence and uniqueness. The strategy's effectiveness is evident in the consistent severity of epidemics, which aligns with the applied curing efforts. Meanwhile, a gradient descent algorithm is proposed to find the optimal curing strategy, which is based on a fixed-point iterative scheme. Finally, to corroborate the theoretical analysis, a series of numerical simulations are conducted. The current results are useful in helping us to understand how multi-strain epidemics behaviors.

With the continuous advancement of computer technology and information storage systems, data structures have become increasingly voluminous and complex, posing significant challenges to data analysis. In practical tasks such as classification and clustering, it has been gradually recognized that while the category information relevant to task objectives typically exhibits concise characteristics, the associated data variables may encompass multiple subclass structures unrelated to current objectives. Conventional methods often neglect these subclass information patterns, resulting in unnecessary information loss. To comprehensively explore the subclass structures within the data, this study proposes a robust t_ν,p distributional factor model (T-DFM) for cluster analysis framework using mixture of Student-t distributions. The proposed T-DFM employs Student-t distribution as clustering factors while emphasizing robustness and interference resistance. T-DFM utilizes a stabilized approach to estimate proportional vectors of distributional factors for observed samples through EM algorithm, enhancing efficiency and accuracy in cluster analysis. Theoretical analysis confirms the algorithmic convergence and robustness of the proposed method. Moreover, extensive experiments conducted on simulated datasets, along with real-world applications of loan approval dataset and air pollution dataset, demonstrate the superior effectiveness and computational efficiency of T-DFM compared to conventional approaches.

This study employs mathematical modeling to analyze the role of combined intervention strategies integrating social distancing and vaccination in epidemic control under Intensive Care Unit (ICU) capacity constraints. Conventional Susceptible–Infected–Removed (SIR) models typically assume a constant total population and often fail to adequately capture the joint effects of viral mutations and demographic dynamics. To address this, we propose an extended SIR model with a Markov-modulated mechanism that accommodates a variable total population and incorporates both deterministic dynamical switching triggered by the emergence of dominant variants and stochastic jump events arising from demographic changes. Within this framework, two stochastic models are developed, differing in how rare events are classified within the jump mechanism. For each model, we first establish mathematical well-posedness, including normalization of population dynamics and proof of positivity for all solution components. The second one is of qualitative and quantitative nature, providing a mathematically rigorous description of regular herd immunity zones with social distancing control when ICU constraints are enforced. The results demonstrate that controlled intervention can sustainably maintain infection levels below the ICU threshold, offering a theoretical basis and policy insights for epidemic management under variant-driven uncertainty.

Feedback serves as a fundamental mechanism that adjusts system input based on measurable information, thereby attenuating the influence of plant uncertainty on system performance. This paper investigates the intrinsic limitations of feedback control for a class of high-order uncertain nonlinear systems. By developing an improved analytical approach, a new difference iteration is derived, whose asymptotic behavior is rigorously shown to govern the divergence properties of the closed-loop system. In contrast to existing results, new quantitative limits on the capability of the feedback mechanism to handle structural uncertainties are then derived based on this iteration. These findings contribute to a deeper understanding of the fundamental capability boundaries of feedback.