Search

Finite difference discretization of the two-dimensional space-fractional diffusion equations derives a complicated linear system consisting of identity matrix and four scaled block-Toeplitz with Toeplitz block (BTTB) matrices resulted from the left and right Riemann–Liouville fractional derivatives in different directions. Incorporating with the diffusion coefficients and the symmetric parts of the BTTB matrices, we construct a diagonal and symmetric splitting (DSS) iteration method, which is demonstrated to be convergent conditionally when the considered space-fractional diffusion equations have sufficiently close diffusion coefficients. By further replacing the symmetric Toeplitz matrices involved in the BTTB matrices with τ matrices, an approximated DSS (ADSS) preconditioner based on two-dimensional fast sine transform is designed to accelerate the convergence rates of the Krylov subspace iteration methods. In this way, the total computational complexity of the ADSS-preconditioned GMRES method will be of O (n 2 log n) , where n 2 represents the dimension of the corresponding discrete linear system. In addition, theoretical analysis demonstrates that the eigenvalues of the ADSS-preconditioned matrix are weakly clustered around a complex disk centered at 1 with the radius less than 1. Numerical experiments show that the ADSS-preconditioned GMRES method is much more efficient than the other existing methods, and can show h -independent convergence behavior. [ABSTRACT FROM AUTHOR]

The document titled "Are you ready for Olympiads? CLASS XII" provides information about the SOF International Mathematics Olympiad for Class XII students. The exam will be held on October 22nd, November 19th, and December 12th, 2024. The syllabus for the exam includes topics such as verbal and non-verbal reasoning, relations and functions, matrices and determinants, continuity and differentiability, integrals, differential equations, vector algebra, three-dimensional geometry, probability, and linear programming. The document also includes sample questions and their solutions. It is recommended to consult additional sources or seek clarification from a mathematics expert to gain a better understanding of the content. [Extracted from the article]

A quiz concerning a practice exam designed for CBSE Class XII students, including multiple choice questions (MCQs), assertion-reason based questions, and case study-based questions.

The article focuses on complex numbers and quadratic equations, providing a comprehensive overview with detailed explanations and visual aids. Topics include complex number operations such as addition, subtraction, and division, the polar and exponential forms of complex numbers, and the characteristics and solutions of quadratic equations.

The article presents the practice paper guide for Mathematics Today's July 2024 edition, focusing on Inverse Trigonometric Functions and Matrices. Topics include detailed question sets covering MCQs, short answer questions, and case studies, aligning with CBSE exam patterns and syllabus updates. It offers comprehensive practice across five sections with varying question types to aid in thorough preparation.

The article presents a comprehensive guide for Joint Entrance Examination (JEE) aspirants focusing on strategies, preparation tips, and solving techniques for various mathematical problems. Topics include calculus and trigonometry, with specific problem-solving approaches. It features contributions from Alok Kumar, an esteemed educator known for training IIT and Olympiad aspirants, providing valuable insights and advanced problem sets designed to enhance students' mathematical proficiency.

The article offers Practice Questions for mathematics Olympiads related to Relations and Functions; Numbers; and Quantitative Aptitude.

A quiz covering multiple-choice questions on various mathematical topics, such as calculus, algebra, trigonometry, and geometry, is presented in the article.

The article primarily focuses on mathematical topics related to permutations, combinations, and determinants, providing detailed theory and high-definition images. It covers factorial notation, important theorems about permutations, properties of combinations, and various applications of combinations in geometry and counting problems.

The article presents questions and answers related to complex numbers and matrices.

The article focuses on identifying conditions under which certain matrices, including null, symmetric, skew-symmetric, and idempotent matrices, satisfy specific properties related to their structure and operations.

We develop a fast convergence iterative method after transforming the Sturm–Liouville problem into the weak-form integral equations, and using sinusoidal functions as the testers as well as the bases of eigenfunction. Owing to the orthogonal property of these bases, we can obtain the expansion coefficients in closed-form. A new idea of orthogonalized and enhanced boundary function (OEBF) is introduced to compute eigenvalues. In the Sobolev space, we prove the closeness of the OEBF to the eigenfunction with their distance being reduced when the eigenvalue increases. Moreover, upon expressing the Rayleigh quotient in terms of OEBF, the unknown functions in the Sturm–Liouville operator can be recovered quickly, merely two boundary data of unknown functions and the first eigenvalue are sufficing. The OEBF is a promising method with a few iterations to obtain quite accurate estimations of the unknown potential and weight functions. Thanks to the symmetry property a symmetric matrix eigenvalue problem is derived to recover a symmetric potential. The characteristic equation endowing with a special coefficient matrix is decomposed into a product of two characteristic equations. The Newton iterative method is thus developed by relying on the product formula to reconstruct the unknown symmetric potential function with the aid of a few lower orders eigenvalues. [ABSTRACT FROM AUTHOR]

A quiz concerning questions for Joint Entrance Examination (JEE) is presented.

In this paper, a novel algorithm for anti-diagonalization of skew symmetric matrices via using orthogonal similarity transformations has been introduced. The theory and algorithm about the anti-triangular factorization of skew-symmetric matrices are proved. In the case of skew-symmetric matrices, we prove that the anti-diagonal form is always obtained, resulting in developing a new factorization scheme. Moreover, a theoretical algorithm is given based on the theory of double eigenvector system, which provides all the information for the factorization of arbitrary matrices. Finally, the proposed algorithm is verified effective and efficient through the numerical experiments of anti-diagonalization of matrices over a general number field. [ABSTRACT FROM AUTHOR]

Research in cognitive science shows that when humans learn concepts, relation-based categories are easier to learn than feature-based categories, and humans can grasp the essential difference of things in different relations and distinguish a certain degree of diversity. For example, in terms of color, blue sea is closer to blue sky than red coral. How can the machine understand the near-far relations among different concepts? Drawing on the idea of granular computing and starting from the perspective of relation, this study proposes a method to describe the spatial near-far relations among different concepts. First, the eigenvalue representation methods of the matrix are given, and on this basis, the salient feature space of the symmetric matrix is proposed. Then, we propose a salient representation method for category, and through qualitative analysis from the perspective of consistency and near-far relations, we find that the salient representation can represent categories from the perspective of attribute and object respectively. Finally, we verify the validity of salient relation representation through second-order isomorphism between intent and extent of concept quantitatively. [ABSTRACT FROM AUTHOR]

The article presents a practice paper quiz for Central Board of Secondary Education (CBSE) aspirants, 2023, consisting of multiple-choice questions related to mathematics, testing their understanding of topics including complex numbers, quadratic polynomials, roots of equations. and more.

A quiz for competency based questions for Central Board of Secondary Education board examinations is presented.

A quiz with mathematical questions on Olympiads for class XII students is presented.

This article investigates the nonnegative consensus tracking problem for networked systems with a distributed static output-feedback (SOF) control protocol. The distributed SOF controller design for networked systems presents a more challenging issue compared with the distributed state-feedback controller design. The agents are described by multi-input multi-output (MIMO) positive dynamic systems which may contain uncertain parameters, and the interconnection among the followers is modeled using an undirected connected communication graph. By employing positive systems theory, a series of necessary and sufficient conditions governing the consensus of the nominal, as well as uncertain, networked positive systems, is developed. Semidefinite programming consensus design approaches are proposed for the convergence rate optimization of MIMO agents. In addition, by exploiting the positivity characteristic of the systems, a linear-programming-based design approach is also proposed for the convergence rate optimization of single-input multi-output (SIMO) agents. The proposed approaches and the corresponding theoretical results are validated by case studies. [ABSTRACT FROM AUTHOR]

This article investigates the synchronization of fractional-order multi-weighted complex networks (FMWCNs) with order $\alpha \in (0,1)$. A useful fractional-order inequality ${}_{t_{0}}^{C} D_{t}^{\alpha } V(x(t))\leq -\mu V(x(t))$ is extended to a more general form ${}_{t_{0}}^{C} D_{t}^{\alpha } V(x(t))\leq -\mu V^{\gamma }(x(t)),\gamma \in (0,1]$ , which plays a pivotal role in studies of synchronization for FMWCNs. However, the inequality ${}_{t_{0}}^{C} D_{t}^{\alpha } V(x(t))\leq -\mu V^{\gamma }(x(t)),\gamma \in (0,1)$ has been applied to achieve the finite-time synchronization for fractional-order systems in the absence of rigorous mathematical proofs. Based on reduction to absurdity in this article, we prove that it cannot be used to obtain finite-time synchronization results under bounded nonzero initial value conditions. Moreover, by using feedback control strategy and Lyapunov direct approach, some sufficient conditions are presented in the forms of linear matrix inequalities (LMIs) to ensure the synchronization for FMWCNs in the sense of a widely accepted definition of synchronization. Meanwhile, these proposed sufficient results cannot guarantee the finite-time synchronization of FMWCNs. Finally, two chaotic systems are given to verify the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In distributed antenna array systems, accurate synchronization of the frequency and phase of the transmission signals among subarrays is a premise for beamforming. To solve this problem, a modified dispersed frequency and phase consensus (MDFPC) algorithm, which is based on differential evolution (DE) and the credibility weighting matrix, is proposed in this paper. DE algorithm is adopted to optimize the mixing matrix of MDFPC algorithm, and the convergence speed of consensus algorithm can be improved. Moreover, Lanczos method is adopted to calculate the fitness of individuals during optimization, thus the computation amount of the eigenvalue decomposition of the large-scale, sparse and symmetric mixing matrix can be effectively reduced. In addition, the influence of the transmission distance between subarrays on the received Signal-to-Noise Ratio (SNR) is considered, and the credibility weighting matrix can be obtained. Then the contribution of low-credible frequency and phase messages to the iterative updated values can be decreased by the credibility weighting matrix, thus more accurate frequency and phase updated values can be obtained in each iteration. It is shown from simulation results that the proposed algorithm can further reduce the phase synchronization error by at least 8% and achieve at least 18% convergence speed improvement compared to dispersed frequency and phase consensus (DFPC) algorithm. [ABSTRACT FROM AUTHOR]

This document is a quiz from the journal "Mathematics Today" and contains a series of math problems. The problems cover various topics such as functions, trigonometry, matrices, linear equations, and probability. The quiz includes questions about finding the range of a function, evaluating limits, solving equations, determining the center and radius of a circle, and calculating probabilities. Readers are encouraged to submit their responses to the journal for a chance to be featured in the next issue. [Extracted from the article]

Semi-supervised symmetric nonnegative matrix factorization (SNMF) has been extensively utilized in both linear and nonlinear data clustering tasks. However, the current SNMF model's non-convex objective function faces challenges in global optimization and time efficiency. In this study, we leverage label information to propose a convex and unconstrained symmetric matrix factorization (SMF) model that is thoroughly analyzed for its convexity properties. In order to capture high-order relationships among data, a hypergraph is utilized in the model, which is computationally simple, translation invariant, and naturally normalized. Moreover, based on the analysis and the corresponding experiments in the paper, the model exhibits robustness towards outliers to some extent. Due to the convexity of our proposed model without constraint, it can be efficiently optimized using the Conjugate Gradient (CG) method, one of the most efficient methods available. Therefore, we propose a novel Convex Combination-based Sufficient Descent CG (CSDCG) method, which outperforms other methods across 284 optimization problems within the CUTEst library. In order to evaluate the effectiveness of the proposed method, the semi-supervised clustering experiments are conducted on the eight datasets by comparison with ten state-of-the-art matrix factorization (MF) methods. The experiment results demonstrate its superiority over the other compared methods to handle the clustering problem with better performance and less computational time. The code is available at https://github.com/Pokemer/HCSSMF. [ABSTRACT FROM AUTHOR]

The DC-DC converter severs as one of the crucial components in DC microgrid applications. In this paper, a novel low frequency current-mode control strategy is proposed to improve overshoot suppression performance for the boost converter against load current and source voltage disturbances. The control strategy is presented as a cascade dual-loop structure composed of a dynamic current-loop controller with asymmetric saturation and a PI form voltage-loop controller. With the low frequency information of disturbances, the designed dynamic current-loop controller delivers not only promising disturbance suppression but also superior reference current tracking. Simulation and experiment results are provided to illustrate the superiority of the proposed strategy on overshoot suppression. [ABSTRACT FROM AUTHOR]

The design of distributed Nash equilibrium-seeking strategies for games in which the involved players are of second-order integrator-type dynamics is investigated in this article. Noticing that velocity signals are usually noisy or not available for feedback control in practical engineering systems, this article supposes that the velocity signals are not accessible for the players. To deal with the absence of velocity measurements, two estimators are designed. The first estimator is established by employing an observer, which has the same order as the players’ dynamics, to estimate the unavailable system states (e.g., the players’ velocities). The second estimator is designed based on a high-pass filter and is motivated by the incentive to reduce the order of the estimator, which in turn saves the computation costs of the seeking algorithms. On the basis of the designed observers/filters, distributed Nash equilibrium-seeking strategies are then established through incorporating them with consensus and gradient algorithms. It is analytically proven that the players’ actions can be regulated to the Nash equilibrium point and their velocities can be regulated to zero by utilizing the proposed velocity-free Nash equilibrium-seeking strategies. A numerical example is provided for the verification of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article is devoted to the problem of detectability of a large class of linear stochastic systems with time varying coefficients simultaneously affected by state multiplicative white noise perturbations and Markovian switching. The main contribution of this article is to propose a Popov–Belevich–Hautus-type test, which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some nonzero output. The proposed setting unifies in some sense the discrete-time and continuous-time ones, dissimilarly to the vast majority of existing works that study discrete and continuous time separately. [ABSTRACT FROM AUTHOR]

This article presents conditions to assure the mean-square stability of linear parameter-varying systems with Markov jumps. The model dynamics are driven not only by a Markov chain but also by time-varying parameters that take values in a polytopic set. No assumption is imposed on how the parameters vary within the polytopic set, i.e., the variation rate can be arbitrarily fast. The proposed conditions stem from a homogeneous polynomial Lyapunov function in the state space, adapted to account for Markov jumps. The stability certificate is sought through linear matrix inequalities. Numerical examples illustrate this article’s contribution. [ABSTRACT FROM AUTHOR]

This article investigates observability of Boolean control networks (BCNs) and probabilistic Boolean networks (PBNs). First, weak observability of BCNs is discussed via the nonaugmented approach. The obtained result is then applied to determine (asymptotic) observability of PBNs. Finally, complexity of algorithms based on new criteria is analyzed. Compared with existing ones, time and space complexity do not get worse, even are improved under some mild conditions. [ABSTRACT FROM AUTHOR]

This article develops the sliding mode control (SMC) strategy for linear impulsive systems with matched disturbances. Such systems describe dynamical systems that evolve according to continuous process most of the time with matched disturbances, but instantaneously exhibit discontinuities, i.e., impulsive disturbances. A suitable sliding surface function is proposed and the resulting sliding mode dynamics are a class of linear impulsive systems. Some sufficient conditions coupled with impulse time sequences are proposed to guarantee the reachability of the predesigned sliding surface and the stability of the reduced-order impulsive systems under sliding motion, respectively. We show how restrictions on the structure of the systems and impulses should be imposed to ensure the feasibility of the proposed SMC strategy in comparison with general SMC in continuous space. To show the effectiveness of the proposed approach, two simulation examples are presented at the end. [ABSTRACT FROM AUTHOR]

The Shapiro scheme, together with the closely related Frisch–Kalman scheme, has been an important approach to system identification and statistical analysis. A longstanding result on this scheme, known as the Shapiro theorem, is both informative and significant. This article imparts a geometric understanding to the Shapiro theorem and generalizes it to the asymmetric setting using the notion of cone-invariance. In particular, we establish the equivalence between two important properties of a real-valued square matrix—irreducible orthant-invariance and simplicity of its dominant eigenvalue under arbitrary diagonal perturbations. The result can be regarded as a converse Perron–Frobenius theorem. Furthermore, we investigate two applications of the proposed result in systems and control, namely, characterization of irreducibly orthant-monotone nonlinear systems and subspace tracking via decentralized control. We also extend the established result to accommodating polyhedral cones and obtain several insights. [ABSTRACT FROM AUTHOR]

In this article, we present a novel approach to reconstruct the topology of networked linear dynamical systems with latent nodes. The network is allowed to have directed loops and bi-directed edges. The main approach relies on the unique decomposition of the inverse of power spectral density matrix (IPSDM) obtained from observed nodes as a sum of sparse and low-rank matrices. We provide conditions and methods for decomposing the IPSDM into sparse and low-rank components. The sparse component yields moral graph (MG) associated with the observed nodes, and the low-rank component retrieves parents, children and spouses (the Markov Blanket) of the hidden nodes. The article provides necessary and sufficient conditions for the unique decomposition of a given skew symmetric matrix into sum of a sparse skew symmetric and a low-rank skew symmetric matrices. For a large class of systems, the unique decomposition of imaginary part of the IPSDM of observed nodes, a skew symmetric matrix, into the sparse and the low-rank components is sufficient to identify the MG of the observed nodes as well as the Markov Blanket of latent nodes. For a large class of systems, all spurious links in the MG formed by the observed nodes can be identified. Assuming conditions on hidden nodes required for identifiability, links between hidden and observed nodes can be reconstructed, thus retrieving the exact topology of the network from the IPSDM. Moreover, for finite data, we provide bounds on entry-wise distance between the true and the estimated IPSDMs. [ABSTRACT FROM AUTHOR]

We study autocovariance least squares (ALS) estimation methods for covariance estimation for linear time-invariant systems. Previous works have posited that calculation of the ALS weighting matrix is intractable unless the number of data points $N_d$ is small because it requires storage of a matrix whose number of elements scales as $N_d^4$. We derive a novel way to compute the weight that avoids this difficulty. In practice, the true optimal weight cannot be calculated because it is a function of the sought covariance matrices. However, our work enables implementation of two novel ALS algorithms that estimate the weight from data. For the purpose of comparison, we also discuss ALS with an arbitrary weight (such as an identity matrix) and present a previously published method for estimating the ALS weight. ALS with an identity weight guarantees unbiased and consistent covariance estimates, but algorithms that estimate the weight from data do not inherit these guarantees. Despite this drawback, we present a numerical example for which the best performing algorithm, iterative estimation of the covariances and the ALS weight, produces covariance estimates with a small amount of bias and a significantly reduced variance compared to all other algorithms. [ABSTRACT FROM AUTHOR]

Due to the “curse of dimensionality” issue, how to discard redundant features and select informative features in high-dimensional data has become a critical problem, hence there are many research studies dedicated to solving this problem. Unsupervised feature selection technique, which does not require any prior category information to conduct with, has gained a prominent place in preprocessing high-dimensional data among all feature selection techniques, and it has been applied to many neural networks and learning systems related applications, e.g., pattern classification. In this article, we propose an efficient method for unsupervised feature selection via orthogonal basis clustering and reliable local structure preserving, which is referred to as OCLSP briefly. Our OCLSP method consists of an orthogonal basis clustering together with an adaptive graph regularization, which realizes the functionality of simultaneously achieving excellent cluster separation and preserving the local information of data. Besides, we exploit an efficient alternative optimization algorithm to solve the challenging optimization problem of our proposed OCLSP method, and we perform a theoretical analysis of its computational complexity and convergence. Eventually, we conduct comprehensive experiments on nine real-world datasets to test the validity of our proposed OCLSP method, and the experimental results demonstrate that our proposed OCLSP method outperforms many state-of-the-art unsupervised feature selection methods in terms of clustering accuracy and normalized mutual information, which indicates that our proposed OCLSP method has a strong ability in identifying more important features. [ABSTRACT FROM AUTHOR]

Based on extensive applications of the time-variant quadratic programming with equality and inequality constraints (TVQPEI) problem and the effectiveness of the zeroing neural network (ZNN) to address time-variant problems, this article proposes a novel finite-time ZNN (FT-ZNN) model with a combined activation function, aimed at providing a superior efficient neurodynamic method to solve the TVQPEI problem. The remarkable properties of the FT-ZNN model are faster finite-time convergence and preferable robustness, which are analyzed in detail, where in the case of the robustness discussion, two kinds of noises (i.e., bounded constant noise and bounded time-variant noise) are taken into account. Moreover, the proposed several theorems all compute the convergent time of the nondisturbed FT-ZNN model and the disturbed FT-ZNN model approaching to the upper bound of residual error. Besides, to enhance the performance of the FT-ZNN model, a fuzzy finite-time ZNN (FFT-ZNN), which possesses a fuzzy parameter, is further presented for solving the TVQPEI problem. A simulative example about the FT-ZNN and FFT-ZNN models solving the TVQPEI problem is given, and the experimental results expectably conform to the theoretical analysis. In addition, the designed FT-ZNN model is effectually applied to the repetitive motion of the three-link redundant robot and image fusion to show its potential practical value. [ABSTRACT FROM AUTHOR]

With the rapid development of swarm intelligence, the consensus of multiagent systems (MASs) has attracted substantial attention due to its broad range of applications in the practical world. Inspired by the considerable gap between control theory and engineering practices, this article is aimed at addressing the mean square consensus problems for stochastic dynamical nonlinear MASs in directed networks by designing proportional-integral (PI) protocols. In light of the general algebraic connectivity, consensus underlying PI protocols for a directed strongly connected network is investigated, and due to the $M$ -matrix approaches, consensus with PI protocols for a directed network containing a spanning tree is studied. By constructing appropriate Lyapunov functions, combining with the stochastic analysis technique and LaSalle’s invariant principles, some sufficient conditions are derived under which the stochastic dynamical MASs realize consensus in mean square. Numerical simulations are finally presented to illustrate the validity of the main results. [ABSTRACT FROM AUTHOR]

Linear complementarity system (LCS) consists of an ordinary differential equation (ODE) and a linear complementarity problem (LCP). In this article, we propose an exponential time-stepping method for solving LCS, which uses exponential integrator to discretize the ODE and solves the LCPs at the discrete time points. Numerical results are reported for illustrating its good performance. [ABSTRACT FROM AUTHOR]

We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system's observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system's state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme. [ABSTRACT FROM AUTHOR]

The goal of this article is to investigate new and simple convergence analysis of dynamic programming for the linear–quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of both matrix inequalities and matrix norm. Under a mild assumption on the initial parameter, we prove that the $Q$ -value iteration exponentially converges to the optimal solution. Moreover, a global asymptotic convergence is also presented. These results are then extended to the policy iteration. We prove that in contrast to the $Q$ -value iteration, the policy iteration always converges exponentially fast. An example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

This article presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error trajectories to tend exponentially fast toward a compact set whenever excitation conditions are satisfied. This algorithm is employed in a large class of problems where unknown parameters are present and are time-varying. It is shown that this algorithm guarantees global boundedness of the state and parameter errors of the system, and avoids an often used filtering approach for constructing key regressor signals. In addition, intervals of time over which these errors tend exponentially fast toward a compact set are provided, both in the presence of finite and persistent excitation. A projection operator is used to ensure the boundedness of the learning rate matrix, as compared to a time-varying forgetting factor. Numerical simulations are provided to complement the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum-seeking algorithm. We propose to use a suitable oscillatory input to modify the system dynamics, at least in an average sense, so as to satisfy a differential linear matrix inequality condition, which in turn guarantees that the system’s state remains inside a prescribed time-varying hyperellipsoid in the state space. The finite-time stability (FTS) of the averaged dynamics implies the FTS of the original system, as the distance between the original and the averaged dynamics can be made arbitrarily small by choosing a sufficiently high value of the dithering frequency used by the extremum-seeking algorithm. The main advantage of the proposed approach resides in its capability of dealing with systems with unknown control direction, and/or with a control direction that changes over time. Being FTS a quantitative approach, this article also gives an estimate of the necessary minimum dithering/mixing frequency provided, and the effectiveness of the proposed finite-time stabilization approach is analyzed by means of numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we consider a collective decision-making process in a network of agents described by a nonlinear interconnected dynamical model with sigmoidal nonlinearities and signed interaction graph. The decisions are encoded in the equilibria of the system. The aim is to investigate this multiagent system when the signed graph representing the community is not structurally balanced and in particular as we vary its frustration, i.e., its distance to structural balance. The model exhibits bifurcations, and a “social effort” parameter, added to the model to represent the strength of the interactions between the agents, plays the role of bifurcation parameter in our analysis. We show that, as the social effort increases, the decision-making dynamics exhibit a pitchfork bifurcation behavior where, from a deadlock situation of “no decision” (i.e., the origin is the only globally stable equilibrium point), two possible (alternative) decision states for the community are achieved (corresponding to two nonzero locally stable equilibria). The value of social effort for which the bifurcation is crossed (and a decision is reached) increases with the frustration of the signed network. [ABSTRACT FROM AUTHOR]

In this article, we study a class of generalized Persidskii systems with external disturbances and establish conditions, in the form of linear matrix inequalities, for input-to-output stability and robust synchronization for these systems. We apply the obtained results to the robust control design for synchronizing linear systems and to the synchronization of Hindmarsh–Rose models of neurons. [ABSTRACT FROM AUTHOR]

In this article, we study the mean-square stabilization of discrete-time multiplicative-noise stochastic systems under decentralized controllers. Two controllers are involved in the system where each controller has access to different information and one information set is contained by another one. The adopted information structure is adapted open-loop. The main contribution of the article is twofold. On one hand, we give the unique explicit solution of the finite-horizon optimization problem in terms of difference Riccati equations. On the other hand, we characterize the equivalent condition for the mean-square stabilization under the decentralized controllers via the corresponding algebraic Riccati equations. Moreover, we derive the optimal and stabilizing solution for the infinite-horizon optimization problem. [ABSTRACT FROM AUTHOR]

This article investigates the event-triggered control problem for switched affine systems (SASs). The presence of affine terms brings many difficulties on the exclusion of triggering Zeno behavior when ensuring asymptotic stability. We propose an event-triggered control strategy dynamically updated with triggering to solve this problem, in which the triggering condition is associated with the affine terms and given with a time-varying term that is updated at triggering instants. Based on the triggering strategy, the controllers for subsystems and a switching rule are designed to achieve asymptotic stability of the resulting closed-loop system. Moreover, due to the special feature of event-triggered SASs, a new method for proving the exclusion of Zeno behavior is given. Finally, the developed results are illustrated by an electric circuit example. [ABSTRACT FROM AUTHOR]

The article investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the article considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares approach—well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix—the article proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized least-squares cost augmented with a proximal-point-type regularization. With the solution of the regularized least-squares problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings. [ABSTRACT FROM AUTHOR]

Model predictive control (MPC) is often tuned by trial and error. When a baseline linear controller exists that is already well tuned in the absence of constraints and MPC is introduced to enforce them, one would like to avoid altering the original linear feedback law whenever they are not active. We formulate this problem as a controller matching similar to the works of Di Cairano and Bemporad (2009), Di Cairano and Bemporad (2010), and Tran et al. (2015), which we extend to a more general framework. We prove that a positive-definite stage-cost matrix yielding this matching property can be computed for all stabilizing linear controllers. In addition, we prove that the constrained estimation problem can also be solved similarly, by matching a linear observer with a moving horizon estimator. Finally, we discuss various aspects of the practical implementation of the proposed technique in some examples. [ABSTRACT FROM AUTHOR]

In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results. [ABSTRACT FROM AUTHOR]

In this article, a data-driven distributed control method is proposed to solve the cooperative optimal output regulation problem of leader–follower multiagent systems. Different from traditional studies on cooperative output regulation, a distributed adaptive internal model is originally developed, which includes a distributed internal model and a distributed observer to estimate the leader’s dynamics. Without relying on the dynamics of multiagent systems, we have proposed two reinforcement learning algorithms, policy iteration and value iteration, to learn the optimal controller through online input and state data, and estimated values of the leader’s state. By combining these methods, we have established a basis for connecting data-distributed control methods with adaptive dynamic programming approaches in general since these are the theoretical foundation from which they are built. [ABSTRACT FROM AUTHOR]

Hash bit selection (HBS) aims to find the most discriminative and informative hash bits from a hash pool generated by using different hashing algorithms. It is usually formulated as a binary quadratic programming problem with an information-theoretic objective function and a string-length constraint. In this article, it is equivalently reformulated in the form of a quadratic unconstrained binary optimization problem by augmenting the objective function with a penalty function. The reformulated problem is solved via collaborative neurodynamic optimization (CNO) with a population of classic discrete Hopfield networks. The two most important hyperparameters of the CNO approach are determined based on Monte Carlo test results. Experimental results on three benchmark data sets are elaborated to substantiate the superiority of the collaborative neurodynamic approach to several existing methods for HBS. [ABSTRACT FROM AUTHOR]

In this article, a novel iterative algorithm is proposed to obtain the positive definite solutions of the discrete coupled Riccati matrix equations. In the presented algorithm, there are no operations of matrix inversion in all iterative steps. Another significant feature of this algorithm is that the latest updated information is used when the current estimation for each unknown matrix is conducted by taking the coupling structure of the discrete coupled Riccati matrix equations into consideration. The convergence performance of the algorithm is also analyzed. Finally, a numerical example is provided to demonstrate the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]