This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems over directed graphs with the constraint of communication bandwidth. Given that there exists an exosystem whose state information is not available to all agents, the authors develop distributed adaptive event-triggered observers for the followers based on relative information between neighboring agents. It should be pointed out that, two kinds of time-varying gains are introduced to avoid relying on any global information associated with the network, and dynamic triggering conditions are designed to get rid of continuous communications. On the basis of the designed observers, the authors devise a local controller for each agent. Compared with the existing related works, the main contribution of the current paper is that the cooperative output regulation problem for general directed graphs is solved requiring neither global information nor continuous communications.

In the field of nonlinear filtering (NLF), it is well-known that the unnormalized conditional density of the states satisfies the Zakai's equation. The splitting-up algorithm has been first studied in the independent noises case by Bensoussan, et al. (1990). In this paper, the authors extend this convergence analysis of the splitting-up algorithm to the correlated noises' case. Given a time discretization, one splits the solution of the Zakai's equation into two interlacing processes (with possibly computational advantage). These two processes correspond respectively to the prediction and updating. Under certain conditions, the authors show that both processes tend to the solution of the Zakai's equation, as the time step goes to zero. The authors specify the conditions imposed on the way of splitting-up to guarantee the convergence. The major technical difficulty in the correlated noises' case, compared with the independent case, is to control the gradient of the second process in some sense. To illustrate the potentially computational advantage of the schemes based on the splitting-up ways, the authors experiment on a toy NLF model using the feedback particle filter (FPF) developed based on the splitting-up method and the sampling importance and resampling (SIR) as comparison. The FPF outperforms in both accuracy and efficiency.

Gas turbine engines must be operated by means of control, and how to achieve multivariable control decoupling with aero-engine control constraints is an open thorny issue attracting increasingly more attention. The paper considers the multivariable decoupling problems of aero-engines by using a compound controller, which originates from the fact that it is impossible to eliminate all the nonlinear dynamics of system to obtain desired constant linear closed-loop system by using full actuated control because of modeling errors and some physical constraints. Two controllers are involved in the compound controller. One is a fully actuated controller and the other is classical feedback controller. In order to use fully actuated control and maintain the accuracy of engine model, a full state scheduling linear parameter-varying (LPV) modeling method is proposed based on fuzzy neural network weights. For a general input matrix of the system, its generalized inverse is applied to design fully actuated controller to result in a pseudolinear system. Combined with a feedback controller and control limiter, the control synthesis is achieved. The simulation shows that the proposed method is possessed of a better decoupling and tracking effect compared with traditional control approach.

In this paper, an adaptive neural tracking control scheme for a class of uncertain switched multi-input multi-output (MIMO) pure-feedback nonlinear systems is proposed. The considered MIMO pure-feedback nonlinear system contains input and output constraints, completely unknown nonlinear functions and time-varying external disturbances. The unknown nonlinear functions representing system uncertainties are identified via radial basis function neural networks (RBFNNs). Then, the Nussbaum function is utilized to deal with the nonlinearity issue caused by the input saturation. To prevent system outputs from violating prescribed constraints, the barrier Lyapunov functions (BLFs) are introduced. Also, a switched disturbance observer is designed to make the time-varying external disturbances estimable. Based on the backstepping recursive design technique and the Lyapunov stability theory, the developed control method is verified applicable to ensure the boundedness of all signals in the closed-loop system and make the system output track given reference signals well. Finally, a numerical simulation is given to demonstrate the effectiveness of the proposed control method.

In this paper, observability is studied for periodically switched Boolean control networks (PSBCNs), which are managed with periodic switching signal and consist of some Boolean control networks. Firstly, via semi-tensor product of matrices, PSBCNs are expressed as algebraic forms. Secondly, a parallel system is constructed by combining two same PSBCNs, based on which, the observability problem of the original PSBCN can be transformed into the set reachability problem of this parallel system. Then, two necessary and sufficient conditions are obtained to detect reachability of parallel systems and observability of PSBCNs. In addition, the proposed conditions are extended to the case of state constraints. Finally, a practical example and a numerical example are provided to illustrate the results.

This paper develops a new fault diagnosis and tolerant control framework of sensor failure (SFDTC) for complex system such as rockets and missiles. The new framework aims to solve two problems: The lack of data and the multiple uncertainty of knowledge. In the SFDTC framework, two parts exist: The fault diagnosis model and the output reconstruction model. These two parts of the new framework are constructed based on the new developed belief rule base with power set (BRB-PS). The multiple uncertainty of knowledge can be addressed by the local ignorance and global ignorance in the new developed BRB-PS model. Then, the stability of the developed framework is proved by the output error of the BRB-PS model. For complex system, the sensor state is determined by many factors and experts cannot provide accurate knowledge. The multiple uncertain knowledge will reduce the performance of the initial SDFTC framework. Therefore, in the SFDTC framework, to handle the influence of the uncertainty of expert knowledge and improve the framework performance, a new optimization model with two optimization goals is developed to ensure the smallest output uncertainty and the highest accuracy simultaneously. A case study is conducted to illustrate the effectiveness of the developed framework.

Yong J [Acta Math. Appl. Sin. Engl. Ser. 28 (2012), 1-30] [Math. Control Relat. Fields 1 (2011), 83-118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperative approach, respectively. The authors extend his results to a singular case. To handle the singularity, the authors prove the solvability of a generalized Riccati equation, and introduce a notion of $\mathbb{MP}$-convergence of matrix. It is shown that the authors can obtain a family of parameter equilibrium controls in both cases. Another interesting outcome is that a new type of parameter forward-backward Volterra integral equations is derived.

This paper is concerned with the input delay compensation problem for neutral-type systems with both state and input delays. Single/various cascaded-observers based output feedback controllers are designed to predict the future states such that the input delay that can be arbitrarily large yet exactly known is compensated completely. Compared with the existing techniques, some more simple necessary and sufficient conditions guaranteeing the stability of the closed-loop systems are offered in terms of the stability of retarded-type time-delay systems referred to as observer-error systems. Finally, the lossless transmission line control system is worked out to illustrate the effectiveness of the proposed controllers.

This paper is concerned with the problem of input-output finite-time guaranteed cost control for a kind of time-varying systems (TVSs). To reduce the transmission burden, an aperiodic-sampling-based event-triggered mechanism is proposed with an adaptive law. And a time-varying Lyapunov functional involving some time-dependent piecewise matrices is designed. Input-output finite-time stability (IO-FTS) conditions are presented for the closed-loop system. By resorting to properties of the matrix polynomial, input-output finite-time stabilization criterions are further derived by recursive linear matrix inequalities. And the sampled-data static output feedback controller can be obtained. In addition, the corresponding optimization problem about minimum values of both the guaranteed cost bound and system output norm are established. Finally, a spring-mass-damper system illustrates the effectiveness and superiority.

In recent years, image processing based on stochastic resonance (SR) has received more and more attention. In this paper, a new model combining dynamical saturating nonlinearity with regularized variational term for enhancement of low contrast image is proposed. The regularized variational term can be setting to total variation (TV), second order total generalized variation (TGV) and non-local means (NLM) in order to gradually suppress noise in the process of solving the model. In addition, the new model is tested on a mass of gray-scale images from standard test image and low contrast indoor color images from Low-Light dataset (LOL). By comparing the new model and other traditional image enhancement models, the results demonstrate the enhanced image not only obtain good perceptual quality but also get more excellent value of evaluation index compared with some previous methods.

This paper deals with the practical exponential stability of two-dimensional (2-D) nonlinear switched positive systems with impulse, disturbance and all modes unstable. Under the mode-dependent interval dwell time switching, new criteria such that 2-D nonlinear switched positive systems achieve practical exponential stability are derived. Furthermore, the explicit upper bound and convergence rate of the system state are estimated explicitly. Numerical examples indicate the correctness and effectiveness of the obtained results.

In this paper, the authors analyze the optimal reinsurance and dividend problem with model uncertainty for an insurer. Here the model uncertainty represents possible deviations between the real market and the assumed model. In addition to the incorporation of model uncertainty into the traditional diffusion surplus process, the authors include a penalty function in the objective function. The proposed goal is to find the optimal reinsurance and dividend strategy that maximizes the expected discounted dividend before ruin in the worst case of all possible scenarios, namely, the worst market. Using a dynamic programming approach, the problem is reduced to solving a Hamilton-Jacob-Bellman-Isaac (HJBI) equation with singular control. This problem is more difficult than the traditional robust control or singular control problem. Here, the authors prove that the value function is the unique solution to this HJBI equation with singular control. Moreover, the authors present a verification theorem when a smooth solution can be found, and derive closed-form solution when the function in the objective function is specified.

Based on bounded rationality, this paper established a price game model of dual channel supply chain composed of manufacturers and retailers. According to the eigenvalue of Jacobi matrix and Jury criterion, the stability of the equilibrium point is analyzed, and then the dynamic evolution process under the parameters of price adjustment speed and retailer's service input is studied through stability region, bifurcation diagram, maximum Lyapunov exponent diagram and attraction basin. The results show that the system enters chaos through flip and Neimark-Sacker bifurcation, and increase of price adjustment speed and service input value will make the system produce more dynamic behavior. In addition, it can be found that the impact of service input value on itself is much greater than that on manufacturers. Secondly, when adjustment speed is selected as bifurcation parameter, the change curve of sales price is inconsistent, in which the change of retailers mainly remains in periodic state, while manufacturers will gradually enter chaos. Finally, studies the evolution of attraction basin in which three kinds of attractors coexist. In particular, coexistence of boundary attractors and internal attractors increases the complexity of system. Therefore, enterprises need to carefully adjust parameters of the game model to control the stability of system and maintain the long-term stability of market competition.

With the increase of economic environment uncertainty, it is of great importance to study the linkage and spillover effects of economic policy uncertainty among countries. Especially, this article selects eight countries along the Belt and Road as the core countries (China, Korea, Croatia, India, Russia, Greece, Pakistan, and Singapore) and four countries (Germany, France, Japan, and UK) as the peripheral countries, and then copula technique and mixed-frequency global vector autoregressive model are employed to analyze the correlation and the spillover effect of the economic policy uncertainty (EPU) for the twelve selected countries, respectively. The proposed empirical findings show clearly that the EPU correlation among the eight core Belt and Road countries is stronger and the spillover effect of the core countries to the peripheral countries is statistically significant. As a result, for harmonious and win-win development, the Belt and Road countries should pay a close attention to the EPU, because the stability of the EPU promotes greatly the economy development.

This paper investigates a multi-period portfolio optimization problem for a defined contribution pension plan with Telser's safety-first criterion. The plan members aim to maximize the expected terminal wealth subject to a constraint that the probability of the terminal wealth falling below a disaster level is less than a pre-determined number called risk control level. By Tchebycheff inequality, Lagrange multiplier technique, the embedding method and Bellman's principle of optimality, the authors obtain the conditions under which the optimal strategy exists and derive the closed-form optimal strategy and value function. Special cases show that the obtained results in this paper can be reduced to those in the classical mean-variance model. Finally, numerical analysis is provided to analyze the effects of the risk control level, the disaster level and the contribution proportion on the disaster probability and the value function. The numerical analysis indicates that the disaster probability in this paper is less than that in the classical mean-variance model on the premise that the value functions are the same in two models.

This paper is to provide a novel approach for the spatial aggregation of judgment matrices. The optimal aggregation method of judgment matrices based on spatial Steiner-Weber point can effectively aggregate the preference information of group members and achieve the optimization of group preference. The method comprises three key elements: The spatial mapping of the judgment matrices, the spatial optimal aggregation model of the judgment matrices, and the plant growth simulation algorithm (PGSA) is used to find the optimal aggregation points. Firstly, the judgment matrices are mapped into a set of spatial multidimensional coordinates by using spatial mapping rules. Secondly, the spatial Steiner-Weber point is used as the prototype to construct the spatial aggregation model. Thirdly, the PGSA algorithm is used to find the spatial aggregation points, whose spatial weighted Euclidean distance to all the decision makers’ preference points is minimal. The optimal aggregation matrix is composed of these optimal aggregation points, which can accurately reflect the decision maker's comprehensive opinions. Finally, the effectiveness and rationality of this method are verified by comparing with the classical group preference aggregation methods.

Misclassified current status data arises if each study subject can only be observed once and the observation status is determined by a diagnostic test with imperfect sensitivity and specificity. For the situation, another issue that may occur is that the observation time may be correlated with the interested failure time, which is often referred to as informative censoring or observation times. It is well-known that in the presence of informative censoring, the analysis that ignores it could yield biased or even misleading results. In this paper, the authors consider such data and propose a frailty-based inference procedure. In particular, an EM algorithm based on Poisson latent variables is developed and the asymptotic properties of the resulting estimators are established. The numerical results show that the proposed method works well in practice and an application to a set of real data is provided.

When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot of data, enjoying high dimension, strong correlation and redundancy, has been generated in real life. So it is necessary to find an effective variable selection method for dealing with collinearity based on the robust method. This paper proposes a penalized $M$-estimation method based on standard error adjusted adaptive elastic-net, which uses $M$-estimators and the corresponding standard errors as weights. The consistency and asymptotic normality of this method are proved theoretically. For the regularization in high-dimensional space, the authors use the multi-step adaptive elastic-net to reduce the dimension to a relatively large scale which is less than the sample size, and then use the proposed method to select variables and estimate parameters. Finally, the authors carry out simulation studies and two real data analysis to examine the finite sample performance of the proposed method. The results show that the proposed method has some advantages over other commonly used methods.

In this study, the authors proposed upper tolerance limits for the gamma mixture distribution based on generalized fiducial inference, and an MCMC simulation is performed to sample from the generalized fiducial distributions. The simulation results and a real hydrological data example show that the proposed tolerance limits are more efficient.

Indirect Pythagorean hodographs (IPH) spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a fractional quadratic transformation. In this paper, the authors provide an algorithm to interactively design a cubic IPH spline curve from any given control polygon. The method has the same friendly interface and properties as those for B-splines, meanwhile facilitates intuitive and efficient construction of open and closed IPH spline curves. The key idea is to solve the ratios of a set of auxiliary points associated with the edges and then construct a piecewise cubic IPH spline curve which has as high as possible continuity, i.e., the absolute curvature value of the adjacent curve segments are the same. A very interesting observation is that for any open control polygon, a quadratic B-spline curve can have continuous absolute curvature by carefully choosing the knots as the function of the control points.

The security of most code-based cryptosystems relies on the hardness of the syndrome decoding (SD) problem. The best solvers of the SD problem are known as information set decoding (ISD) algorithms. Recently, Weger, et al. (2020) described Stern's ISD algorithm, $s$-blocks algorithm and partial Gaussian elimination algorithms in the Lee metric over an integer residue ring ${\bm Z}_{p^m}$, where $p$ is a prime number and $m$ is a positive integer, and analyzed the time complexity. In this paper, the authors apply a binary ISD algorithm in the Hamming metric proposed by May, et al. (2011) to solve the SD problem over the Galois ring $GR(p^m, k)$ endowed with the Lee metric and provide a detailed complexity analysis. Compared with Stern's algorithm over ${\bm Z}_{p^m}$ in the Lee metric, the proposed algorithm has a significant improvement in the time complexity.

Impossible differential cryptanalysis is an important approach to evaluate the security of block ciphers. In EUROCRYPT 2016, Sun, et al. proved that there exists no impossible differential longer than four rounds for the AES structure where $S$-boxes are arbitrary. In DCC 2019, Wang, et al. proved that any differential is possible for 5-round AES, assuming that the round keys are independent and uniformly random. In ASIACRYPT 2020, Hu, et al. used automatic search to show that there exists no one-byte active impossible differential for 5-round AES-128 considering the relations of 3-round keys. By algebraic methods, this paper theoretically proves that there exists no one-byte active impossible differential for 5-round AES even considering the relations of all round keys. Firstly, the authors prove the independence of ten bytes in the consecutive four round keys under the key schedule of AES-128. Then 5-round AES is decomposed to three subfunctions and the propagations of the considered differences in these subfunctions are discussed. Finally, the authors prove that the considered differential trails can be connected by the ten bytes of round keys. Furthermore, for any given one-byte active differential, there are at least $2^{51}$ master keys such that the differential is possible for 5-round AES-128.