Monotonic optimization is a special class of global optimization with applications cross fields. It addresses problems in which the objective and constraint functions are increasing w.r.t. each of the variables. In this work, we extend to the case where the objective and constraint functions are monotonic. We present a general framework to address such problems, and especially propose a complete algorithm that is guaranteed to terminate in finitely many steps for problems in a special form. Different from traditional optimization algorithms based on gradient descent, our algorithm does not require closed-form expressions of the functions. As an important application, the functions involved in the parameter optimization problem of LWE-based encryption scheme exhibit monotonicity w.r.t. each of the variables (but may not be increasing), and certain functions involved have no closed-form expression. Inspired by the idea of mathematics mechanization, we formalize practical problems into mathematical models and provide a framework for developing automatic and systematic approaches to tackle the parameter optimization problems in lattice-based cryptography. As an illustrative example, we consider the parameter optimization of BGV scheme in the context of minimizing communication overhead, without considering homomorphic operations, and provide optimal parameters for it under specified security levels and correctness probabilities.

This paper investigates the problem of event-triggered disturbance attenuation and fault-tolerant constrained consensus in multi-agent systems with a variable number of agents. First, an event-triggered design combining a disturbance observer and a fault-tolerant controller is proposed, which reduces network bandwidth usage while accurately estimating and compensating for disturbances and partial actuator failures, thereby improving system reliability. Next, a time-varying impulsive Lyapunov function related to the number of agents is introduced, and the communication matrix changes—resulting from variations in the communication structure—are transformed into additive uncertainties, thus addressing topology switching issues arising from changes in the number of agents. To overcome the limitation of traditional $H_\infty$ control, which assumes zero initial conditions, a performance index dependent on the initial state is proposed, along with a novel event-triggered disturbance-rejection fault-tolerant control protocol. Sufficient conditions ensuring the consistency of disturbance attenuation and fault-tolerance constraints are then provided. Numerical simulations demonstrate the effectiveness of the proposed method.

This paper delves into the determination of the optimal safety loading that an insurer ought to incorporate into reinsurance pricing. We base our analysis on the assumption that the insurer utilizes a specific form of the loss function and is confronted with losses that adhere to a zero - corrected exponential distribution. This assumption is steered by the expected premium principle. By minimizing the Value at Risk (VaR) of the insurer's liabilities and the Conditional Tail Expectation (CTE) risk measures, our research investigates the optimal safety loading principle for reinsurance premiums. This approach aims to curtail the potential losses that are associated with the insurer's premiums. Our research outcomes reveal that the results obtained from the VaR and CTE risk measures bear substantial significance in the real - world insurance and reinsurance markets.

In this paper, we address the problem of almost sure polynomial stabilization for a class of highly nonlinear stochastic systems via sampled-data feedback. The considered systems fall within a general framework that includes two key features: (a) continuous-time irreducible Markov chain- we introduce a continuous-time irreducible Markov chain to describe systems that can undergo sudden alterations in their parameters and structures. This flexibility allows us to model real-world scenarios more accurately; (b) diffusion and drift coefficients with polynomial growth - unlike existing literature that primarily focuses on systems with bounded delays, we investigate the stabilization conditions for highly nonlinear stochastic systems with pantograph delay, an unbounded delay. Specifically, we analyze systems where the diffusion and drift coefficients satisfy a polynomial growth condition. To achieve our goal, we employ M-matrix theory and Lyapunov functions as basic tools. Our main results establish that the system can attain almost sure polynomial stabilization through a subtly and innovatively designed sampled-data feedback. We validate our theoretical findings with numerical simulations, demonstrating the effectiveness of our approach. This work contributes to the understanding of stabilization in highly nonlinear stochastic systems, particularly those with unbounded delays, and broadens the practical applicability of stochastic modeling.

This article aims to establish a Bayesian Stackelberg game framework for analyzing the incomplete information demand response management with overlapping electricity sales areas, and further provide the corresponding equilibrium strategies. Considering that the satisfaction parameters of power users are private, a Bayesian game model is constructed among these power users, and a non-cooperative game model is established due to the price competition of microgrids. To ensure the sequential interactions of demand response, a Stackelberg game is developed by assuming that the microgrids are leaders and the power users are followers, and the Bayesian Nash equilibrium and Stackelberg equilibrium are proved to exist and are unique under some conditions. In addition, the Bayesian Nash equilibrium for power users is obtained using the fictitious play method in the symmetrical case, and an iterative algorithm is presented for determining the Stackelberg equilibrium. Finally, the numerical simulations are provided showing the effectiveness and convergence of the iterative algorithm, which indicates that our approach can enhance profits for microgrids while ensuring power supply and demand balance.

This paper applies the Cheng projection to the support vector machine (SVM) in handling missing data. In the process of handling missing data, each sample with missing values is replaced by its Cheng projection in the original space. Additionally, two classification algorithms for handling linearly separable and nonlinearly separable datasets with missing data are presented. For linearly separable datasets with missing data, Cheng kernel function is introduced, and an SVM classification algorithm that improves the linear kernel function to the Cheng kernel function is proposed. For nonlinearly separable datasets, a generalized Gaussian Radial Basis Function kernel is introduced and an SVM classification algorithm for handling missing data is given. For both algorithms, two comparative experiments are conducted to demonstrate their effectiveness.

This study revisits Hotelling's $T^2$ (HT) tests for one- and two-sample mean problems, introduces a family of scaled Hotelling's $T^2$-type tests and develops two omnibus tests, termed Omnibus Hotelling's $T^2$ (HT-O), for both cases. Furthermore, we analyze the powers of the HT-O tests through the asymptotic null distributions of the scaled Hotelling's $T^2$-type tests. Extensive simulation results demonstrate that the proposed HT-O tests effectively control Type I error and maintain high power under complex correlation structures, outperforming the classical HT tests in various scenarios. Applications to anti-depressant imipramine efficacy and $\alpha$-amylase activity further highlight the superior performance and practical utility of the HT-O tests.

In this paper, a finite-time adaptive neural networks relative event-triggered command-filtered tracking control for the stochastic nonlinear systems with the signals constraint is presented. Firstly, the unknown nonlinear functions are approximated using neural networks radial basis function, and the barrier Lyapunov function is utilized to ensure the output signal constraint within a predefined range. Secondly, a finite-time command-filtered approach is adopted in the controller design to achieve finite-time stability. Thirdly, a relative threshold event-triggered mechanism is introduced to reduce the communication costs, and the threshold parameters are dynamically adjusted in response to the actual tracking performance, thereby enhancing the adaptability and efficiency of the control strategy. Finally, simulation results demonstrate the effectiveness of the proposed control method.

The composite anti-disturbance $ H_{\infty} $ control problem for switched descriptor systems with multiple disturbances is investigated in this paper. One disturbance is modeled by an exogenous system with perturbations, while the other is norm-bounded. Firstly, based on generalized Sylvester equations, a novel reduced-order disturbance observer is proposed to estimate the unmeasurable state and modeling disturbance. Meanwhile, a composite anti-disturbance controller, consisting of a disturbance compensator and an estimated state-based controller, is developed based on the outputs of the proposed reduced-order disturbance observer. Then, under multi-Lyapunov functions and mode-dependent average dwell time, sufficient conditions are presented to ensure that the closed-loop switched descriptor systems are regular, impulse-free, globally uniformly exponentially stable with a weighted $H_{\infty}$ performance. Further, the design method of reduced-order disturbance observer and anti-disturbance controller is proposed by an algorithm. Finally, the superiority and practicality of the developed results are demonstrated through a numerical example and a Boost converter circuit in wind power system.

Classical linear discriminant analysis (LDA) (Fisher, 1936) implicitly assumes the classification boundary depends on only one linear combination of the predictors. This restriction can lead to poor classification in applications where the decision boundary depends on multiple linear combinations of the predictors. To overcome this challenge, we first project the predictors onto an envelope central space and then perform LDA based on the sufficient predictor. The performance of the proposed method in improving classification accuracy is demonstrated in both synthetic data and real applications.

This paper examines whether the parametric regression model is correctly specified for both source and target data and whether the regression pattern in the source domain aligns with that of the target domain. This evaluation is a critical prerequisite for applying model-based transfer learning methods under covariate shift assumptions. Traditional regression model checks and two-sample regression tests are insufficient to address this issue. To overcome these limitations, we propose a novel adaptive-to-regression test statistic that is asymptotically distribution-free. Under the null hypothesis, the test follows a chi-square weak limit, preserving the significance level and enabling critical value determination without resampling techniques. Additionally, we systematically analyze the test's power performance, highlighting its sensitivity to different sub-local alternatives that deviate from the null hypothesis. Numerical studies, including simulations, assess finite-sample performance, and a real-world data example is provided for illustration.

Distributed learning is a well-established method for estimation tasks over extensively distributed datasets. However, non-randomly stored data can introduce bias into local parameter estimates, leading to significant performance degradation in classical distributed algorithms. In this paper, we propose a novel Distributed Quasi-Newton Pilot (DQNP) method for distributed learning with non-randomly distributed data. The proposed approach accommodates both randomly and non-randomly distributed data settings and imposes no constraints on the uniformity of local sample sizes. Additionally, it avoids the need to transfer the Hessian matrix or compute its inversion, thereby greatly reducing computational and communication complexity. We theoretically demonstrate that the resulting estimator achieves statistical efficiency under mild conditions. Extensive numerical experiments on synthetic and real-world data validate the theoretical findings and illustrate the effectiveness of the proposed method.

Quantile regression (QR) has become an important tool to measure dependence of response variable's quantiles on a number of predictors for heterogeneous data, especially heavy-tailed data and outliers. However, it is quite challenging to make statistical inference on distributed high-dimensional QR with missing data due to the distributed nature, sparsity and missingness of data and non-differentiable quantile loss function. To overcome the challenge, this paper develops a communication-efficient method to select variables and estimate parameters by utilizing a smooth function to approximate the non-differentiable quantile loss function and incorporating the idea of the inverse probability weighting and the penalty function. The proposed approach has three merits. First, it is both computationally and communicationally efficient because only the first- and second-order information of the approximate objective function are communicated at each iteration. Second, the proposed estimators possess the oracle property after a limited number of iterations without constraint on the number of machines. Third, the proposed method simultaneously selects variables and estimates parameters within a distributed framework, ensuring robustness to the specified response probability or propensity score function of the missing data mechanism. Simulation studies and a real example are used to illustrate the effectiveness of the proposed methodologies.

This article investigates the fuzzy adaptive resilient leader-following consensus control problem for a class of nonlinear heterogeneous multi-agent systems (HMASs) under denial-of-service (DoS) attacks. Since the considered leader's system contains unknown nonlinear dynamics and HMASs are subject to DoS attacks, the leader's states and output are inaccessible to followers, a stable distributed estimator is developed to estimate them. To solve the virtual controller non-differentiable problem in backstepping control design technique caused by DoS attacks, the command-filter is introduced into the backstepping control design process, and formulate a resilient leader-following consensus controller. It is proven that the proposed control scheme can guarantee that the controlled HMASs are stable, and the consensus errors converge to a small neighborhood of zero. Finally, a simulation example on unmanned aerial vehicle-unmanned ground vehicles (UAV-UGVs) is provided to verify the feasibility of the proposed control scheme.

In this paper, the asynchronously practical control is studied for discrete time switched systems with singular perturbations. Firstly, a novel Lyapunov function is constructed including the singular perturbation parameter and quasi-time parameter matrices. And then, quasi-time dependent criteria are achieved to study the practical stability and asynchronous stabilization; an allowable upper bound is expected to be obtained for the singular perturbation parameters; the asynchronous sampling controller is designed with quasi-time gains, and the application range of this controller is further widened via some constraints relaxed. At last, two simulation examples are utilized to illustrate that the proposed results are less conservative and effective.

This paper first proposes a distributed continuous-time Newton-Raphson algorithm for heterogeneous linear multi-agent systems over unbalanced digraphs. Then this approach extends to cases where the local cost functions and Hessian matrices are unknown. While local exponential stability of the inverse Hessian matrix estimator has been established for single-agent systems, this paper proves local exponential stability in multi-agent systems, ensuring the stability of the proposed distributed Newton-Raphson extremum seeking algorithm. A numerical example demonstrates the effectiveness of the proposed algorithms.

In this paper, we stumble upon that the normal ordering expansion for $\left(x\frac{\mathrm{d}}{\mathrm{d}x}\right)^n$ is equivalent to the expansion of $(bD_G)^n$, where $G$ is the context-free grammar defined by $G=\{a\rightarrow a, b\rightarrow 1\}$. Motivated by this fact, we introduce the definition of grammatical basis. We then study several grammatical bases generated by $G=\{a\rightarrow 1, b\rightarrow 1\}$. Using grammatical bases, we give a classification of grammars. In particular, we provide new grammatical descriptions for Ward numbers, Hermite polynomials, Bessel polynomials, Chebyshev polynomials and logarithmic polynomials arising from an integral. We end this paper by giving some applications of grammatical bases. One can see that if two or more polynomials share a grammatical basis, then they share the same coefficients, and it might be helpful for the detection of intrinsic relationship among superficially different structures.

In this paper, we are concerned with the problem of achieving Nash equilibrium in noncooperative games over networks. We propose two types of distributed projected gradient dynamics with accelerated convergence rates. The first type is a variant of the commonly-known consensus-based gradient dynamics, where the consensual terms for determining the actions of each player are discarded to accelerate the learning process. The second type is formulated by introducing the Nesterov's accelerated method into the distributed projected gradient dynamics. We prove convergence of both algorithms with at least linear rates under the common assumption of Lipschitz continuity and strongly monotonicity. Simulation examples are presented to validate the outperformance of our proposed algorithms over the well-known consensus-based approach and augmented game based approach. It is shown that the required number of iterations to reach the Nash equilibrium is greatly reduced in our proposed algorithms. These results could be helpful to address the issue of long convergence time in partial-information Nash equilibrium seeking algorithms.

This paper studies the adaptive mean-square output consensus problem of heterogeneous multi-agent systems with different multiplicative noises under a directed graph. Specifically, due to the presence of packet losses, the optimal estimator is first derived for the continuous-time stochastic system through discretization to estimate each agent's state. Based on this, we design an edge-based distributed adaptive control protocol that is independent of global information of the communication topology. With the aid of the distributed feedforward control approach and stochastic stability theory, the sufficient condition for achieving mean-square output consensus is derived. Moreover, the convergence of the optimal estimator is analyzed through rigorous mathematical derivation. Finally, a numerical simulation verifies the validity of the obtained results.

This paper proposes a factor model for interval-valued panel data. We exploit that the first $r$ largest eigenvalues of the sample covariance matrix divided by $N$ (i.e., $\frac{\langle s_Y^{\prime},s_Y\rangle_K}{NT}$) of interval-valued response variables are $O_p(1)$, while the rest are $o_p(1)$. Then the eigenvalue ratio-type estimators of the number of factors are proposed. Under certain conditions, the proposed estimators are all proven to be consistent. Moreover, the estimators of interval-valued factors and the loadings can be obtained by the principal components method. Monte Carlo simulation studies show that the proposed estimators have the desired finite sample properties. A real example is analysed for illustrations.

In this paper, we address the bounded leader-following consensus problem for linear multi-agent systems connected via undirected graphs, specifically in the presence of non-consistent time-varying communication delays. The periodic event-triggered scheme is proposed to mitigate the adverse effects of these delays, which ensures discrete data transmission only occurs at specific event instants. By leveraging the nature of periodic event-triggered schemes, Zeno-freeness can be guaranteed by discretely event-checking. Additionally, the appropriate design of the threshold range prevents the event-triggered consensus from degrading into sampled-data consensus. The numerical simulation is presented in the end to show the effectiveness of the provided approach.

This article explores the dynamic event-triggered (DET) ${H_\infty }$ load frequency control (LFC) for networked power systems (NPSs) subject to deception attacks. Firstly, a novel DET mechanism is proposed, which aims to improve the system control performance under deception attacks and save more network resources effectively. Compared with the existing DET mechanisms, the proposed DET mechanism involves an adaptive rule, which can be utilized to dynamically adjust the event-triggered threshold based on the relative rate of change and absolute difference of system state and the frequency of deception attacks. Then, considering the complexity of the actual power systems, a new DET-based LFC stochastic model is formulated, which integrates actuator failure, network-induced delay and deception attacks. Subsequently, by using Lyapunov theory, the sufficient conditions guaranteeing the asymptotic mean-square stability of the NPSs are derived. Finally, some simulation results are presented to validate the superiority of the designed approach.

The broad goal of the research surveyed in this article is to develop methods for understanding the aggregate behavior of interconnected dynamical systems, as found in mathematical physics, neuroscience, economics, power systems and neural networks. Questions concern prediction of emergent (often unanticipated) phenomena, methods to formulate distributed control schemes to influence this behavior, and these topics prompt many other questions in the domain of learning. The area of mean field games, pioneered by Peter Caines, are well suited to addressing these topics. The approach is surveyed in the present paper within the context of controlled coupled oscillators.

This paper addresses boundary control to input-to-state stabilization for fractional convection-diffusion-reaction (FCDR) systems governed by coupled time fractional partial differential equations (TFPDEs) under matched and unmatched disturbances over actuator/sensor networks using output feedback, fractional sliding mode (FSM) algorithm and sampled-in-space sensing. Here it is assumed that sensors provide discrete in space measurements, i.e., spatially averaged measurements (SAMs), and a limited number of sensors are allocated in a spatial domain. A sampled-data observation problem is first in investigation, which contains to design a FSM observer against boundary disturbances and to prove input-to-state stability (ISS) of the proposed observer. Using this observer and backstepping approach, we develop an output feedback FSM controller and establish the reaching condition to FSM surface. Using the fractional Lyapunov method, ISS of the closed-loop dynamics is achieved. Theoretical results are verified by numerical simulations.

The authors study an approximation method for partially observed Markov decision processes (POMDPs) with continuous spaces. Belief MDP reduction, which has been the standard approach to study POMDPs requires rigorous approximation methods for practical applications, due to the state space being lifted to the space of probability measures. Generalizing recent work, in this paper the authors present rigorous approximation methods via discretizing the observation space and constructing a fully observed finite MDP model using a finite length history of the discrete observations and control actions. The authors show that the resulting policy is near-optimal under some regularity assumptions on the channel, and under certain controlled filter stability requirements for the hidden state process. The authors also provide a Q learning algorithm that uses a finite memory of discretized information variables, and prove its convergence to the optimality equation of the finite fully observed MDP constructed using the approximation method.

This paper considers the practical fixed-time tracking control problem for a state constrained pure-feedback nonlinear system. A new barrier function is first proposed to handle various asymmetric time-varying constraints and unify the cases with and without state constraints. Then a low-cost neural network based adaptive fixed-time controller is constructed by further combining the dynamic surface control, which overcomes the technical problems of overparametrization and singularity in the backstepping procedure. Our design guarantees that the tracking error converges to a small neighbourhood of zero in a fixed time while satisfying the state constraints as a priority task without imposing feasibility conditions on the virtual controllers. Simulation results validate the effectiveness of the proposed adaptive fixed-time tracking control strategy.

With the development of the tourism industry, the associated carbon dioxide emissions have become considerable, significantly impacting global climate change. This study will compile relevant publications from various fields in recent years on sustainable tourism and climate change, and analyse the hot issues in this field based on the bidirectional relationship between the tourism industry and climate change. Firstly, based on the research framework of the bidirectional relationship between tourism and climate change, the impact of the tourism industry on climate change was measured from the perspective of tourist carbon footprint in four aspects. Simultaneously, the effects of climate change on the tourism industry were summarized. Subsequently, bibliometric methods are employed to analyse the literature in this field in recent years. Finally, combining qualitative and quantitative review results, the study presents feasible suggestions for future research directions, highlighting potential avenues for further investigation from both technical and policy perspectives.

This paper considers risk-sensitive linear-quadratic mean-field games. By the so-called direct approach via dynamic programming, we determine the feedback Nash equilibrium in an $N$-player game. Subsequently, we design a set of decentralized strategies by passing to the mean-field limit. We prove that the set of decentralized strategies constitutes an $O(1/N)$-Nash equilibrium when applied by the $N$ players, and hence obtain so far the tightest equilibrium error bounds for this class of models.

In this paper, the authors revisit decentralized control of linear quadratic (LQ) systems. Instead of imposing an assumption that the process and observation noises are Gaussian, the authors assume that the controllers are restricted to be linear. The authors show that the multiple decentralized control models, the form of the best linear controllers is identical to the optimal controllers obtained under the Gaussian noise assumption. The main contribution of the paper is the solution technique. Traditionally, optimal controllers for decentralized LQ systems are identified using dynamic programming, maximum principle, or spectral decomposition. The authors present an alternative approach which is based by combining elementary building blocks from linear systems, namely, completion of squares, state splitting, static reduction, orthogonal projection, (conditional) independence of state processes, and decentralized estimation.

Optimal feedback control of nonlinear system with free terminal time present many challenges including nonsmooth in the value function and control laws, and existence of multiple local or even global optimal trajectories. To mitigate these issues, the authors introduce an actor-critic method along with some enhancements. The authors demonstrate the algorithm's effectiveness on a prototypical example featuring each of the main pathological issues present in problems of this type as well as a higher dimensional example to show that the solution method presented can scale.

This study aims to solve the Nash equilibrium (NE) seeking problem for monotone $N$-coalition games. The authors assume that the gradient mapping of the game is monotone but not necessarily strictly or strongly monotone. Such a merely monotone assumption presents significant challenges to NE seeking, since the basic gradient descent method may fail to converge. The authors start with a regularization-based projected gradient dynamical system in a general non-cooperative game framework and analyze the convergence of the dynamics under different scenarios. Then, the authors develop NE seeking algorithms for monotone $N$-coalition games with undirected and connected inner-coalition communication graphs. Asymptotic convergence to the least-norm NE is proven. The convergence rate of the algorithm for an analytic mapping is provided. Furthermore, the authors propose a novel regularization-based dynamical system that allows different parameters among the coalitions. Rigorous analysis and a numerical example are provided to illustrate the effectiveness of the proposed method.

In this paper the authors consider the operational problem of optimal signalling and control, called control-coding capacity (with feedback), $C_{FB}$ in bits/second, of discrete-time nonlinear partially observable stochastic systems in state space form, subject to an average cost constraint. $C_{FB}$ is the maximum rate of encoding signals or messages into randomized controller-encoder strategies with feedback, which control the state of the system, and reproducing the messages at the output of the system using a decoder or estimator with arbitrary small asymptotic error probability. In the first part of the paper, the authors characterize $C_{FB}$ by an information theoretic optimization problem of maximizing directed information from the inputs to the outputs of the system, over randomized strategies (controller-encoders). The authors derive equivalent characterizations of $C_{FB}$, using randomized strategies generated by either uniform or arbitrary distributed random variables (RVs), sufficient statistics, and a posteriori distributions of nonlinear filtering theory. In the second part of the paper, the authors analyze $C_{FB}$ for linear-quadratic Gaussian partially observable stochastic systems (LQG-POSSs). The authors show that randomized strategies consist of control, estimation and signalling parts, and the sufficient statistics are, two Kalman-filters and an orthogonal innovations process. The authors prove a semi-separation principle which states, the optimal control strategy is determined explicitly from the solution of a control matrix difference Riccati equation (DRE), independently of the estimation and signalling strategies. Finally, the authors express the optimization problem of $C_{FB}$ in terms of two filtering matrix DREs, a control matrix DRE, and the covariance of the innovations process. Throughout the paper, the authors illustrate that the expression of $C_{FB}$ includes as degenerate cases, problems of stochastic optimal control and channel capacity of information transmission.

This paper considers the value iteration algorithms of stochastic zero-sum linear quadratic games with unkown dynamics. On-policy and off-policy learning algorithms are developed to solve the stochastic zero-sum games, where the system dynamics is not required. By analyzing the value function iterations, the convergence of the model-based algorithm is shown. The equivalence of several types of value iteration algorithms is established. The effectiveness of model-free algorithms is demonstrated by a numerical example.

This paper proposes a data-driven learning-based approach to predictive control for switched nonlinear systems subject to state and control constraints and external stochastic disturbances. A switched Koopman modeling framework is developed, where a multi-mode neural network for state lifting is trained simultaneously with Koopman operators and state reconstruction matrices for all the modes. This framework facilitates the construction of a switched linear Koopman model in a transformed space and effectively captures the dynamics of the original nonlinear system. A switched predictive control strategy is then designed to regulate the switched Koopman model with constrained state and control inputs against both the stochastic disturbances and the uncertainties introduced by the lifting neural network. The proposed control scheme ensures mean-square stability and guarantees boundedness during the online phase. Furthermore, boundedness analysis is performed to determine the reachable set of the original system state across all admissible switching sequences. The effectiveness of the proposed methodology is demonstrated through a case study of a gene regulatory network.

This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions. In this context, a binary-valued measurement represents whether the measured value is smaller than a fixed threshold. Meanwhile, the "intermittent|" scenario arises when there is a non-zero probability of not detecting each local function value during the measuring process. Using this kind of coarse measurement, we propose a discrete-time stochastic extremum seeking-based algorithm for distributed optimization over a directed graph. As is well-known, many existing distributed optimization algorithms require a doubly-stochastic weight matrix to ensure the average consensus of agents. However, in practical engineering, achieving double-stochasticity, especially for directed graphs, is not always feasible or desirable. To overcome this limitation, we design a row-stochastic matrix and a column-stochastic matrix as weight matrices in our algorithm instead of relying on doubly-stochasticity. Under some mild conditions, we rigorously prove that agents can reach the average consensus and ultimately find the optimal solution. Finally, we provide a numerical example to illustrate the effectiveness of our algorithm.

In this paper, we consider a wave-plate transmission system on Riemannian manifold with boundary controls on the plate equation. This model arises from the noise control and is extended to the broader context of the Riemannian manifold. By employing the semigroup method, we obtain the well-posedness of the system. Subsequently, under certain geometric conditions, we establish a polynomial energy decay estimate of type $t^{-1}$ by using the geometric multiplier method in which the conclusion proposed by Guo and Yao (J. Math. Anal. Appl. 2006, 317: 50-70.) plays a crucial role in our proof. It effectively addresses the challenge posed by curvature on the Riemannian manifold. Moreover, by employing the higher-order energy method, we overcome the technical difficulties caused by higher-order terms in boundary controls, which generalizes the results in the literature.

In this paper, we consider a class of linear quadratic optimal control problems of backward stochastic differential equations under partial information with initial value constraint. The main contribution is to obtain an explicitly optimal controller by using a Riccati equation and an optimal parameter characterized by a matrix equation. The key technique is to introduce Lagrange multiplier to transform the problem with initial value constraint into unconstrained optimal control problem and optimal parameter calculation problem, and solve the optimal parameter calculation by using the exact controllability of the system.

This paper addresses an indefinite linear-quadratic mean field games for stochastic large-population system, where the individual diffusion coefficients may depend on both the state and the control of the agents. Moreover, the control weights in the cost functionals could be indefinite. We employ a direct approach to derive the $\epsilon$-Nash equilibrium strategy. First, we formally solve an $N$-player game problem within a vast but finite population setting. Subsequently, by introducing two Riccati equations, we decouple or reduce the high-dimensional systems to yield centralized strategies, which depend on the state of a specific player and the average state of the population. As the population size $N$ goes infinity, the construction of decentralized strategies becomes feasible. Then, we demonstrate that these strategies constitute an $\epsilon$-Nash equilibrium. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed strategies.

In this paper, the issues of both reconstructibility analysis and state estimation are investigated for locally reconstructible Boolean networks (BNs), where the pinning control is employed to design a special control sequence. First, this paper will focus on dealing with state unreconstructible cycle based on state set-estimation theory, and the concept of set-to-set reachability is proposed. Second, the locally reconstructible BNs are transformed to Boolean control networks (BCNs) by pinning control technique, where a logical matrix is designed by a special algorithm such that all states in the unreconstructible initial state set can evolve into the reconstructible state set, simultaneously. Third, a sufficient condition for the existence of a free Boolean control sequence is obtained, which guarantees that a locally reconstructible BN can be transformed into a reconstructible one. Besides, an optimization control algorithm is proposed to generate pinning control sequence and further optimize the reconstructibility of BNs. A kind of pinning control-based state estimation method is also developed. Finally, an example is provided to show the feasibility of the proposed methods.

This paper investigates an innovative predefined time output feedback adaptive fuzzy consensus control method for fractional-order nonlinear multi-agent systems(FONMASs). The controlled system includes unmeasurable states and unknown nonlinear functions. The fuzzy state observer is built to evaluate unmeasurable state variables, unknown nonlinear functions are addressed through fuzzy logic system approximation. Combining with fractional-order dynamic surface control (DSC) and the theory of stability of predefined time, the control method is raised. By employing FODSC techniques, the computational explosion problem can be avoided. The stability of the closed-loop system is analyzed using the Lyapunov function, demonstrating that FONMAS achieves semi-global practical predefined time stability (SGPPTS). Eventually, the validity of the prescribed control strategy is verified by a simulation case.