This paper focuses on the disturbance suppression issue of hidden semi-Markov jump systems leveraging composite control. The system consists of a semi-Markov layer and an observed mode sequence layer, and it is subject to a matched disturbance generated by an exogenous system and a mismatched disturbance that is norm bounded. The proposal is to design a composite controller based on a disturbance observer to counteract and attenuate the disturbances effectively. By constructing a special Lyapunov function comparison point, the exponential stability is analyzed with the stability criterion in the form of linear matrix inequality is established. Two simulation examples are provided to demonstrate the practical merits of the composite controller relative to the single H_∞ control.

It is with great pleasure and admiration that we celebrate the 60th birthday of Professor Lihua Xie, a distinguished researcher and visionary leader in the field of robust control and estimation. Prof. Xie’s remarkable journey, marked by outstanding achievements and groundbreaking contributions, has left an indelible mark on the world of engineering and academia.
Prof. Xie’s academic odyssey began at Nanjing University of Science and Technology, where he earned his bachelor’s and master’s degrees in 1983 and 1986, respectively. His pursuit of knowledge led him to the University of Newcastle, Australia, where he obtained his PhD in 1992. Since 1992, he has been a cornerstone of Nanyang Technological University (NTU), Singapore, currently serving as a distinguished professor in the School of Electrical and Electronic Engineering and as the Director of the Centre for Advanced Robotics Technology Innovation (CARTIN), NTU.
One of Prof. Xie’s pivotal contributions lies in the realm of robust control and estimation. His early work in the early 1990s addressed robust solutions for systems with parametric uncertainties, providing a profound understanding of how uncertainty influences control system performance. His pioneering research not only illuminated the impact of uncertainty but also offered effective strategies, particularly for parametric uncertainty, ensuring the robustness of control systems. Prof. Xie was among the first to develop robust estimation techniques for systems grappling with parametric uncertainties, influencing researchers globally since the 1990s.
In the past two decades, Prof. Xie, alongside his co-author, established a groundbreaking equivalence between quantized feedback and robust control. This breakthrough extended the applicability of existing robust control theory to the analysis and design of control systems operating under quantized feedback. His work also unraveled the intricate interplay among data rate, network topology, and agent dynamics in multi-agent consensus - a fundamental challenge in cooperative control. Prof. Xie’s research provided answers to crucial questions, such as determining the minimal data rate and network topology for multi-agent consensus, along with corresponding coding and decoding schemes.
The spectrum of Prof. Xie’s impact extends to compressive sensing, where he and his student established a phase transition relationship between sparsity and recoverability for complex signals. Their continuous compressive sensing algorithms and Vandermonde decomposition theory for multi-level Toeplitz matrices have found applications in array signal processing, marking another significant milestone in his illustrious career.
Beyond theoretical endeavors, Prof. Xie’s practical innovations have revolutionized localization and unmanned systems. His research group’s developments include a WiFi-based indoor positioning system, multi-modality sensor fusion technology, and a fully integrated navigation solution for UAVs. These innovations have found applications in diverse fields, from structure inspection and delivery using UAVs to a low-cost universal navigation system for AGVs in logistics and manufacturing.
In the realm of research and development leadership, Prof. Xie’s impact is equally profound. He is the founding Director of the Delta-NTU Corporate Laboratory for Cyber-physical Systems, which focuses on the development of smart manufacturing and smart learning technologies for industry. Additionally, Prof. Xie established the Centre for Advanced Robotics Technology Innovation, where he currently serves as the Director. The center’s mission is to pioneer advanced sensing and perception technologies, as well as collaborative robotics technologies, with applications in logistics, manufacturing, and elderly care.
As an accomplished researcher, Prof. Xie has demonstrated unparalleled dedication to serving the research community. His extensive editorial roles, including a founding Editor-inChief for Unmanned Systems and Associate Editor for Sciences China - Information Science, showcase his commitment to advancing scientific knowledge. He has played pivotal roles in various editorial boards, such as IET Book Series in Control and esteemed journals like IEEE Transactions on Automatic Control and Automatica.
Prof. Xie’s impact extends beyond editorial responsibilities; he has been a distinguished IEEE Distinguished Lecturer, a Board of Governors member for the IEEE Control System Society, and Vice President since January 2024. His leadership roles also include serving as General Chair of significant conferences, including the 62nd IEEE Conference on Decision and Control in December 2023.
His professional achievements, recognized by peers worldwide, include fellowships in the Academy of Engineering Singapore, the Institute of Electrical and Electronics Engineers (IEEE), International Federation of Automatic Control (IFAC), and the Chinese Automation Association (CAA).
In celebration of Prof. Xie’s 60th birthday, we invited 17 papers from friends and colleagues for this special issue. As editors, we extend our deepest gratitude to all the authors for their invaluable contributions. Special thanks to the Journal of Systems Science & Complexity editorial office, including Prof. Xiao-Shan Gao (Editor-in-Chief), Prof. Yanlong Zhao (Managing Editor), and Ms. Guoyun Wu (Editorial Director), for their steadfast support from the conception to the publication of this special issue.
On this momentous occasion, we express our profound appreciation for Prof. Lihua Xie for his unwavering commitment to advancing knowledge and look forward to the continued brilliance and innovation in the next chapters of his illustrious career.
Happy Birthday, Prof. Lihua Xie!

This paper is devoted to stabilizing the high-order uncertain nonlinear system in a fixed time by output feedback control. First, a novel settling time solution method is proposed by establishing an indirect double system and using the comparison principle. Then a fixed-time observer and a neural networked based adaptive law are constructed to estimate the state and the unknown disturbance for the high-order uncertain nonlinear system. Furthermore, a fixed-time output feedback controller is proposed via the homogeneity technique. The upper bound of the settling time is analyzed for the closed-loop system under the proposed output feedback control. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.

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.

This paper investigates the networked evolutionary games (NEGs) with profile-dependent delays, including modeling and stability analysis. Profile-dependent delay, which varies with the game profiles, slows the information transmission between participants. Firstly, the dynamics model is proposed for the profile-dependent delayed NEG, then the algebraic formulation is established using the algebraic state space approach. Secondly, the dynamic behavior of the game is discussed, involving general stability and evolutionarily stable profile analysis. Necessary and sufficient criteria are derived using the matrices, which can be easily verified by mathematical software. Finally, a numerical example is carried out to demonstrate the validity of the theoretical results.

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, several equivalent forms of the well-known Brockett's second example system are firstly presented. The stabilization of the system is then treated in the fully actuated system approach. A simple continuous time-invariant sub-stabilizing controller is designed, and the corresponding region of attraction is characterized. As a result, all trajectories of the system starting from the characterized region of attraction are driven exponentially to the origin. Since the region of attraction is very large, the designed sub-stabilizing controller can be directly useful in many practical situations. In cases where the initial values are indeed needed to be chosen out of the region of attraction, extremely simple pre-controllers can be designed, which drive the system trajectories into the designed region of attraction. A simulation of the designed control system is carried out to show the effect of the proposed approach.

This paper studies the real-time optimal state estimation-based feedback control for twolevel stochastic quantum systems in the non-Markovian case. The system model is established by combining the time-convolutionless non-Markovian master equation and the stochastic master equation. A nonlinear filter based on the state-dependent Riccati equation is designed in order to achieve the realtime optimal estimation of quantum states. A quadratic function multiplied with an exponential term is selected as the Lyapunov function, and a continuous-time control law is deduced via the stochastic Lyapunov stability theorem to realize eigenstate feedback control based on real-time optimal state estimation. Numerical simulation results illustrate that the proposed control scheme is capable of steering the two-level quantum system from an arbitrary initial state to the desired eigenstate with a fidelity higher than 99% within a time of 3 a.u.

The cross-dimensional dynamical systems have received increasing research attention in recent years. This paper characterizes the structure features of the cross-dimensional vector space. Specifically, it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space. Hence, it means that one can isometrically and linearly embed the cross-dimensional vector space into the $\ell^{2}$, which is known as the space of square summable sequences. This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.

This paper mainly investigates the security problem of a networked control system based on a Kalman filter. A false data injection attack scheme is proposed to only tamper the measurement output, and its stealthiness and effects on system performance are analyzed under three cases of system knowledge held by an attacker and a defender. Firstly, it is derived that the proposed attack scheme is stealthy for a residual-based detector when the attacker and the defender hold the same accurate system knowledge. Secondly, it is proven that the proposed attack scheme is still stealthy even if the defender actively modifies the Kalman filter gain so as to make it different from that of the attacker. Thirdly, the stealthiness condition of the proposed attack scheme based on an inaccurate model is given. Furthermore, for each case, the instability conditions of the closed-loop system under attack are derived. Finally, simulation results are provided to test the proposed attack scheme.

Xinjiang’s agriculture is a typical irrigated agriculture for its agriculture water consumption accounts for 96% of the total water use. As a typical resource-deficient area, the key to Xinjiang’s agricultural development is saving water. This paper takes the high-efficient water-saving irrigation technology of 41 regions along the Tarim River from 2002 to 2013 as the research object, adopts spatial stochastic frontier model to measure the space efficiency of high-efficient water-saving irrigation technology, and analyzes the effect of water-saving irrigation technology on agricultural development. Results show that the water-saving irrigation technology has a spatial effect, if neglecting it, the error of missing variables will occur, and the average loss will be 6.98 percentage points. The spatial correlation effect promotes the improvement of the efficiency of water-saving irrigation technology. The spatial heterogeneity leads to the spatial imbalance of the efficiency of water-saving irrigation technology. The promotion of agricultural water-saving irrigation technology can increase production and the efficiency of agricultural development. Due to the technical heterogeneity of different types of water-saving irrigation technology, the contribution to the development of agriculture is also different. The study finds that water-saving irrigation technology of drip irrigation in the Tarim River contributes more to agricultural development.

In this paper, a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost functionals. The coefficients in the state equation and the weighting matrices in the cost functionals are all deterministic. Closed-loop strategies are introduced, which require to be independent of initial states; and such a nature makes it very useful and convenient in applications. The follower first solves a stochastic linear quadratic optimal control problem, and his optimal closed-loop strategy is characterized by a Riccati equation, together with an adapted solution to a linear backward stochastic differential equation. Then the leader turns to solve a stochastic linear quadratic optimal control problem of a forward-backward stochastic differential equation, necessary conditions for the existence of the optimal closed-loop strategy for the leader is given by a Riccati equation. Some examples are also given.

Generalized linear models are usually adopted to model the discrete or nonnegative responses. In this paper, empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated. Under some mild conditions, the consistency and asymptotic normality of the maximum empirical likelihood estimator are established, and the asymptotic χ² distribution of the empirical log-likelihood ratio is also obtained. Compared with the existing results, the new conditions are more weak and easy to verify. Some simulations are presented to illustrate these asymptotic properties.

This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy discrete systems with input delays and cyber attacks. The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties. By considering the influences of input delays and stochastic cyber attacks, a newly fuzzy robust controller is established. Afterward, the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional. Afterward, a solving algorithm for obtaining the controller gains is given. Finally, the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.

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 many application fields of regression analysis, prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients. In this paper, the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions. By combining series approximation method, twostage least squares method and Lagrange multiplier method, the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties. Furthermore, the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions, and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses. Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples. Furthermore, a real example is provided to illustrate the application of the proposed estimation and testing methods.

The intra-cluster lag consensus means that the agents in the same cluster can achieve lag consensus asymptotically while the agents in different clusters can achieve different consensus. In this paper, the authors investigate the observer-based intra-cluster lag consensus problems of multi-agent systems (MASs) with general linear dynamics and nonlinear dynamics via intermittent adaptive pinning control. The interaction network is considered to be weakly connected, i.e., it is not necessary to be strongly connected, in-degree balanced or contain a directed spanning tree. To realise the intra-cluster lag consensus, a class of observers is designed to estimate the states of followers. Then a class of observer-based intermittent adaptive pinning control protocols is proposed according to the difference that the agents receive information source. Moreover, the pinning gains are designed to be intermittent adaptive and have an exponential convergence rate, which will effectively reduce communication costs, avoid the pinning gains being larger than those needed in real applications and guarantee the pinning gains quickly converge to steady value. Correspondingly, some sufficient consensus criteria are derived and rigorous proofs are given based on matrix theory and Lyapunov stability theory. Finally, the effectiveness for the proposed intermittent adaptive pinning control strategy is validated by a numerical simulation.

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.

In this paper, the strong structural controllability of the leader-follower framework is discussed. Firstly, the authors analyze different edge augmentation methods to preserve the strong structural controllability of the path-bud topology. The following four cases are considered: Adding edges from the path to the bud; adding edges from the bud to the path; adding the reverse or forward edges to the path or bud; and adding both the reverse and forward edges to the path or bud. Then sufficient conditions are derived for the strong structural controllability of the new topologies which are generated by adding different edges. In addition, it is proved that rank[A B] = n is a necessary condition for the strong structural controllability. Finally, three examples are given to verify the effectiveness of the main results.

The estimates of the high-dimensional volatility matrix based on high-frequency data play a pivotal role in many financial applications. However, most existing studies have been built on the sub-Gaussian and cross-sectional independence assumptions of microstructure noise, which are typically violated in the financial markets. In this paper, the authors proposed a new robust volatility matrix estimator, with very mild assumptions on the cross-sectional dependence and tail behaviors of the noises, and demonstrated that it can achieve the optimal convergence rate n^-1/4. Furthermore, the proposed model offered better explanatory and predictive powers by decomposing the estimator into low-rank and sparse components, using an appropriate regularization procedure. Simulation studies demonstrated that the proposed estimator outperforms its competitors under various dependence structures of microstructure noise. Additionally, an extensive analysis of the high-frequency data for stocks in the Shenzhen Stock Exchange of China demonstrated the practical effectiveness of the estimator.

The attitude control and momentum management (ACMM) problem is quite fundamental for many spacecrafts including space stations, sky laboratories and etc. Instead of single attitude control problem, ACMM problem has to take account of both disturbance rejection and energy optimization. This paper studies the ACMM problem for general spacecraft. A practical active disturbance rejection control architecture is proposed with hierarchical compensation to different kinds of uncertain dynamics or disturbances. In particular, by integrating RLS into ESO, the constant and sinusoidal disturbance terms to be compensated are reconstructed. Also, the LQR law is implemented to achieve the desired performance of control systems after disturbance compensation. Furthermore, quantitative performances of the generalized ESO, the RLS algorithm and the closed-loop tracking system are rigorously analyzed. Finally, the results under 9-DOF semi-physical test environment show the effectiveness of our control method.

The output regulation control problem for the Markovian jump systems with colored-noise is proposed in this paper. Since the modes mismatch problem often exists in the Markovian switching system, the authors design a modes asynchronous controller with an internal model form, which can not only deal with external disturbance, but also reduce the influence of stochastic noise on the system, such that the mean square of the regulation error can be made arbitrarily small by turning the designed parameters. Meanwhile, a criterion of the m-th moment noise-to-state exponential stability is presented for continuous-time Markovian jump systems under the asynchronous control.

In this paper, the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered. With the help of stochastic approximation algorithms with expanding truncations, the authors give the recursive estimates for the parameters of both the linear system and the binary sensor. Under reasonable conditions, all constructed estimates are proved to be convergent to the true values with probability one, and the convergence rates are also established. A simulation example is provided to justify the theoretical results.

This paper proposes a robust two-stage estimation procedure for a general spatial dynamic panel data model in light of the two-stage estimation procedure in Jin, et al. (2020). The authors replace the least squares estimation in the first stage of Jin, et al. (2020) by M-estimation. The authors also provide the justification for not making any change in its second stage when the number of time periods is large enough. The proposed methodology is robust and efficient, and it can be easily implemented. In addition, the authors study the limiting behavior of the parameter estimators, which are shown to be consistent and asymptotic normally distributed under some conditions. Extensive simulation studies are carried out to assess the proposed procedure and a COVID-19 data example is conducted for illustration.

This paper discusses feedback Stackelberg strategies for the continuous-time mean-field type stochastic systems with multiple followers in infinite horizon. First, optimal control problems of the followers are studied in the sense of Nash equilibrium. With the help of a set of generalized algebraic Riccati equations (GAREs), sufficient conditions for the solvability are put forward. Then, the leader faces a constrained optimal control problem by transforming the cost functional into a trace criterion. Employing the Karush-Kuhn-Tucker (KKT) conditions, necessary conditions are presented in term of the solvability of the cross-coupled stochastic algebraic equations (CSAEs). Moreover, feedback Stackelberg strategies are obtained based on the solutions of the CSAEs. In addition, an iterative scheme is introduced to obtain efficiently the solutions of the CSAEs. Finally, an example is given to shed light on the effectiveness of the proposed results.

Quantized feedback control is fundamental to system synthesis with limited communication capacity. In sharp contrast to the existing literature on quantized control which requires an explicit dynamical model, the authors study the quadratic stabilization and performance control problems with logarithmically quantized feedback in a direct data-driven framework, where the system state matrix is not exactly known and instead, belongs to an ambiguity set that is directly constructed from a finite number of noisy system data. To this end, the authors firstly establish sufficient and necessary conditions via linear matrix inequalities for the existence of a common quantized controller that achieves our control objectives over the ambiguity set. Then, the authors provide necessary conditions on the data for the solvability of the LMIs, and determine the coarsest quantization density via semi-definite programming. The theoretical results are validated through numerical examples.

Multiple response regression model is commonly employed to investigate the relationship between multiple outcomes and a set of potential predictors, where single-response analysis and multivariate analysis of variance (MANOVA) are two frequently used methods for association analysis. However, both methods have their own limitations. The basis of the former method is independence of multiple responses and the latter one assumes that multiple responses are normally distributed. In this work, the authors propose a test statistic for multiple response association analysis in high-dimensional situations based on F statistic. It is free of normal distribution assumption and the asymptotic normal distribution is obtained under some regular conditions. Extensive computer simulations and four real data applications show its superiority over single-response analysis and MANOVA methods.

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.

This paper proposed a general framework based on semiparametric additive mixed effects model to identify subgroups on each covariate and estimate the corresponding regression functions simultaneously for longitudinal data, thus it could reveal which covariate contributes to the existence of subgroups among population. A backfitting combined with k-means algorithm was developed to detect subgroup structure on each covariate and estimate each semiparametric additive component across subgroups. A Bayesian information criterion is employed to estimate the actual number of groups. The efficacy and accuracy of the proposed procedure in identifying the subgroups and estimating the regression functions are illustrated through numerical studies. In addition, the authors demonstrate the usefulness of the proposed method with applications to PBC data and Industrial Portfolio’s Return data and provide meaningful partitions of the populations.

The cube attack proposed by Dinur and Shamir is one of the most important key-recovery attacks against Trivium. Recently division property based cube attacks have been extensively studied and significantly improved. In particular, the MILP modeling technique for the three-subset division property without unknown subset proposed by Hao, et al. at EUROCRYPT 2020 and the new technique with nested monomial predictions proposed by Hu, et al. at ASIACRYPT 2021 are best techniques to recover exact superpolies in division property based cube attacks. Consequently, at this state of the art, whether a superpoly can be recovered in division property based cube attacks is mainly decided by the scale of the superpoly, that is, the number of terms. Hence the choice for proper cubes corresponding to low-complexity superpolies is more critical now. Some effective cube construction methods were proposed for experimental cube attacks, but not applicable to division property based cube attacks. In this paper, the authors propose a heuristic cube criterion and a cube sieve algorithm, which can be combined with the three-subset division property to recover a number of superpolies. Applied to 815-round Trivium, the authors recovered 417 superpolies from 441 cubes obtained by our algorithm of sizes between 41 and 48. The success rate is 94.56%. There are 165 non-constant superpolies with degree less than 14. In order to demonstrate the significance of the new algorithm, the authors tested the best superpoly recovery technique at EUROCRYPT 2020 using random cubes of similar sizes on 815-round Trivium. The experimental result shows that no cube could be completely recovered within a given period of time because the superpolies for random cubes are too complex.

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 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.

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.

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.

This paper studies the cluster consensus of multi-agent systems (MASs) with objective optimization on directed and detail balanced networks, in which the global optimization objective function is a linear combination of local objective functions of all agents. Firstly, a directed and detail balanced network is constructed that depends on the weights of the global objective function, and two kinds of novel continuous-time optimization algorithms are proposed based on time-invariant and timevarying objective functions. Secondly, by using fixed-time stability theory and convex optimization theory, some sufficient conditions are obtained to ensure that all agents’ states reach cluster consensus within a fixed-time, and asymptotically converge to the optimal solution of the global objective function. Finally, two examples are presented to show the efficacy of the theoretical results.

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.

The issue of stability and group consensus tracking is investigated for the discrete-time heterogeneous networked multi-agent systems with communication constraints (e.g., time delays and data loss) in this paper. Firstly, the couple-group consensus tracking control is analyzed theoretically, the communication constraints are compensated by the prediction method, and the factor of leaders is introduced to make the system not lose generality. Secondly, the necessary and sufficient condition is given to ensure the stability of the system and achieve the couple-group consensus tracking control, and relax the topology constraint of in-degrees balance by cooperative-competitive interactions. In addition, the result of couple groups is extended to multiple groups based on the predictive control protocol. Numerical simulations with Matlab show that the proposed networked predictive control can effectively overcome the network constraints, the dynamic performance and control effect are better than the general control without the prediction.

The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered observations. The authors adopt a direct approach, i.e., without identifying the unknown parameters and functions within the systems, adaptive regulators are directly designed based on the event-triggered observations on the regulation errors. The adaptive regulators belong to the stochastic approximation algorithms and under moderate assumptions, the authors prove that the adaptive regulators are optimal for both the Hammerstein and Wiener systems in the sense that the squared regulation errors are asymptotically minimized. The authors also testify the theoretical results through simulation studies.

This paper studies the formation control problem for the second-order heterogeneous nonlinear multi-agent systems (MASs) with switching topology and quantized control inputs. Compared with formation control under the fixed topology, under the switching topology inherent nonlinear dynamics of the agent and the connectivity change of the communication topology are considered. Moreover, to avoid the chattering phenomenon caused by unknown input disturbances, the hysteretic quantizers are incorporated to quantize the input signals. By using the Lyapunov stability theory and leader-follower formation approach, the proposed formation control scheme ensures that all signals of the MASs are semi-globally uniformly ultimately bounded (SGUUB). Finally, the efficiency of the theoretical results is proved by a simulation example.