This paper develops a game-theoretic framework to analyze the strategic interaction among insurers, reinsurers, and catastrophe (CAT) bond investors in the market for catastrophe risk transfer. We model the cost determination and allocation of reinsurance and CAT bonds as a two-stage game. In the first stage, the reinsurer and the CAT bond investor engage in a non-cooperative Nash game to determine the costs of reinsurance and CAT bonds. In the second stage, the insurer acts as a follower, optimizing its reinsurance retention and CAT bond purchase strategies based on the prices set by the reinsurer and the investor. All players are assumed to have mean-variance preferences. We derive closed-form solutions for the optimal strategies and the Nash equilibrium, and examine how key parameters, such as risk aversion coefficients and the basis risk correlation, affect the equilibrium outcomes. Our numerical analysis reveals that the insurer’s risk aversion significantly influences the overall cost of risk transfer, while the correlation between claims and the CAT bond trigger index does not negatively affect the price of the CAT bond. The model provides insights into the substitutability and complementarity of reinsurance and CAT bonds, with implications for insurers, investors, and regulators in designing efficient risk transfer mechanisms.

This paper focuses on resilient output formation control for heterogeneous linear multiagent systems subject to denial-of-service (DoS) attacks. A control framework is developed to guarantee prescribed-time convergence under directed communication topology. To address the scenario where follower agents have no access to the leader’s system dynamics, a prescribed-time observer is developed based on the time-varying scaling function, which enables accurate estimation of the leader’s system matrix within a predefined time interval. Building upon this, a distributed prescribed-time resilient compensator is designed to enhance cooperative behavior among agents in the presence of DoS attacks. Sufficient conditions are derived to guarantee that the compensator accurately estimates and tracks the leader’s state under DoS attacks. Furthermore, a prescribed-time controller is proposed such that the resilient output formation tracking problem can be solved within the desired convergence time. Finally, numerical simulations are provided to verify the prescribed-time convergence of the proposed approach.

In this paper, we investigate the multi-cluster flocking of the Cucker-Smale system with external perturbation. First, when the external perturbation satisfies the Lipschitz condition, the system achieves the multi-cluster flocking. Second, due to introducing task strategy, each subgroup can reach their respective target velocity. Then, during the flocking process, it is proved that collision avoidance can be achieved both between subgroups and within each subgroup. Finally, the correctness of the theoretical analysis is verified through numerical simulation.

Model reference adaptive control (MRAC) has experienced substantial theoretical development. However, the existing research on MRAC based quadcopters remains largely confined to simulations, and outdoor real-world flight validations, especially those for adaptive fault-tolerant control (AFTC), have yet to be systematically studied. To address this issue, this paper pioneers the development of a direct AFTC framework by integrating MRAC with a fault compensation mechanism for quadcopters subject to any single unknown time-varying rotor fault. The rotor faults under consideration include step-change and continuous variations in thrust, and are formulated by linear parametrizations. This formulation enables online adaptation of the fault compensation parameters through a Lyapunov-based parameter update law. Then, a fault-tolerant MRAC law is designed, in which a dedicated fault compensation mechanism is integrated to effectively mitigate the adverse effects of unknown rotor faults. A Lyapunov-based stability analysis establishes the boundedness of all closed-loop signals and asymptotic tracking of the reference attitudes. Finally, outdoor flight experiments are conducted using a Pixhawk-based quadcopter platform. Experimental results illustrate that the proposed AFTC method maintains stable flight and high-precision attitude tracking, exhibiting significant improvements compared to the non-fault-tolerant design.

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.

The in-orbit service of flexible spacecraft is important for space technology. Precise attitude control and vibration suppression affect spacecraft performance, mission success, and lifespan. This paper focuses on attitude tracking and vibration suppression for flexible spacecraft with input and distributed disturbances and saturation. We use the virtual work principle and accounted for damping to derive partial differential equations (PDEs) and boundary conditions for flexible spacecraft. For the complex, flexible spacecraft system, a prescribed-performance adaptive robust control method is developed that integrates attitude tracking and vibration suppression by combining compound disturbance estimation and compensation. Through two-point control, finite-time stability is achieved for such infinite-dimensional distributed-parameter systems with rigid-flexible coupling. The finite-time stability and convergence of the closed-loop system under the proposed control scheme are proved utilizing Lyapunov theory. By comparing with numerical simulations under conventional PID control, the effectiveness and performance advantages of the control design were validated. This study provides a promising control framework for achieving high-performance control of complex disturbed flexible spacecraft.

Multi-point aggregation with evolving task states is a representative allocation problem in multi-unmanned platform systems. This paper studies an offline multi-UGV setting in which all fire tasks are detected at t = 0, but their states evolve during travel and cooperative service. A bi-objective model minimizes makespan and resource consumption cost while distinguishing geometric distance, traversal risk, and non-traversability. Cooperative service is arrival-aware: each UGV contributes upon arrival, and subsequent arrivals incrementally alter the task-state evolution rate. A dual-mode crossover and secondary-mutation NSGA-II (DCSM-NSGA-II) is developed. According to parental structural similarity, crossover applies either an order-preserving sequence mode or a bounded union-intersection allocation mode; secondary mutation is triggered when standard mutation leaves the allocation structure unchanged. Simulations use 30 matched independent runs, a fixed representative-solution rule, and normalized empirical-reference-front indicators. Across three scales, DCSM-NSGA-II achieves the best mean HV and IGD and the lowest mean representative makespan and cost, with paired tests showing clear gains over several alternative operators. In an additional 20-task/12-UGV case, it achieves the best mean values for all four measures, although its HV and IGD differences from standard NSGA-II remain nonsignificant after multiple-testing correction.

Moving planes and moving quadrics have become effective algebraic tools in the implicitization of rational surfaces, widely applied to problems such as curve/surface implicitization, surface intersection, and singular point computation. Currently, algorithms for computing moving planes for rational surfaces are relatively straightforward, while the computation of moving quadrics remains challenging. First, we propose a type theorem for minimal bases of moving quadrics for bi-degree (m, n) rational surfaces without base points, proving that any moving quadric can be generated from moving planes. Second, we construct a correspondence between moving plane modules and moving quadric modules by defining γ-matrix, and demonstrate their application in surface implicitization. Finally, based on moving plane tables and moving quadric tables, we propose a hierarchical construction theory for moving quadrics. By selecting layer-by-layer computed moving quadrics and their corresponding moving planes, we construct a series of coefficient matrices of order 2mn-kn (0 ≤ k ≤ 2m-µ_2n), achieving surface implicitization.

With the increasing penetration of renewable energy and the growing diversity of frequency regulation resources, load frequency control is increasingly challenged by heterogeneous dynamics, load disturbances, and model uncertainties. To address these issues, an adaptive zone barrier Lyapunov function-based load frequency control method is proposed for interconnected power systems with heterogeneous resources. A free-zone mechanism is introduced into the barrier Lyapunov framework. As a result, unnecessary control actions are avoided when the frequency deviation remains within the free zone. The controller is activated only when the deviation enters the boundary-regulation region, thereby preventing constraint violation. Fuzzy logic systems are employed to approximate unknown nonlinearities and composite disturbances. An improved Bezier curve-based optimization algorithm is used to tune the controller parameters. Then, a multi-objective optimization framework is formulated to balance power deviation suppression, regulation mileage payment, and carbon emission cost. The effectiveness and robustness of the proposed method are verified under load disturbances, model uncertainties, and renewable regulation resource shortages.

This paper studies output-type stability properties for time-delay systems within the inputto-state stability framework. We derive sufficient conditions based on Lyapunov–Krasovskii functionals (lkf) with pointwise dissipation rates under a uniform bounded-input bounded-state (u-bibs) assumption. When the output coincides with the state, the u-bibs assumption is unnecessary, extending a classical Lyapunov result to a robust setting. We further establish an lkf-based condition with pointwise dissipation rates for an input-to-output stability property. These results relax the standard lkf-based sufficient conditions by incorporating pointwise dissipation rates into the convergence analysis of the functionals along trajectories.

This paper introduces a new adaptive input design method for system identification under binary sensors. The design method employs the complexity measure derived from Fisher information in choosing optimal inputs for identification of gain systems as well as joint estimation of system gains and measurement biases. The identification method is formulated in the framework of persistent identification that requires sustained identification capability for all time segments of different starting times. Since the optimal input depends on the unknown system parameters, input design must be carried out adaptively in real-time identification applications. Computation of the related Fisher information matrices, input adaptation algorithms with embedded joint parameter estimation are developed. Two adaptation schemes are introduced, one using stochastic approximation algorithms, and the other employing two-time-scale ideas. Key properties of the algorithms are presented. Benefits and implementation of the algorithms are demonstrated by simulation examples.

This paper proposes a network double autoregressive model by integrating network structure into the double autoregressive framework, which enables simultaneous characterization of the dynamic effects of network connections and autoregressive terms on both conditional mean and conditional heteroscedasticity of multivariate time series. For parameter estimation, a self-weighted quasi-maximum likelihood estimator is adopted to relax moment requirements and adapt to heavy-tailed financial data. The asymptotic properties of the estimator are derived under both interior and boundary conditions of the parameter space. A Lagrange Multiplier (LM) test is proposed for zero volatility coefficients, which maintains a χ² asymptotic distribution regardless of whether the nuisance parameters lie on the boundary or not. Finite-sample simulations demonstrate that the proposed method delivers satisfactory performances. Empirical analysis on daily log returns of stocks from China’s A-share market further reveals that the NDAR model performs comparably to competing approaches.

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.