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.

In this note, a benchmark example system which is not stabilizable by a smooth state feedback controller is considered with the fully actuated system (FAS) approach. It is shown that a smooth controller exists which drives the trajectories starting from a large domain in the initial value space to the origin exponentially. Such a result brings about a generalization of Lyapunov asymptotical stability, which is termed as global exponential sub-stability. The region of attraction is allowed to be an unbounded open set of the initial values with closure containing the origin. This sub-stability result may be viewed to be superior to some local stability results in the Lyapunov sense because the region of attraction is much larger than any finite ball containing the origin and meanwhile the feasible trajectories are always driven to the origin exponentially. Based on this sub-stabilization result, globally asymptotically stabilizing controllers for the system can be provided in two general ways, one is through combination with existing globally stabilizing controllers, and the other is by using a pre-controller to first move an initial point which is not within the region of attraction into the region of attraction.

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!

Aiming to improve the pull-up control performance in the process of releasing balloonborne solar powered UAVs (Unmanned Aerial Vehicles), this paper establishes the full flight mechanics equations with flexible modes, and proposes the control method suitable for engineering application. To be specific, the authors first calculate the real aerodynamic force on horizontal stabilizer by comparing the fuselage deformation in ballooning test with that in static loading test. Furthermore, considering fuselage elastic deformation, the pitching moment coefficient is obtained and the influence of airspeed and elevator angle on pitching moment coefficient and control surface efficiency are analysed. Second, the authors establish a complete flight mechanics model, including elastic structural dynamic model and rigid flight dynamic model, by comprehensively considering the aerodynamic data, the relationship between fuselage deformation and load, as well as the ballooning test. Third, the authors perform the numerical simulation and comparison study on control performance between rigid model and flexible model. Moreover, the authors implement model modification based on the low altitude flight test and steady-state point analysing. Finally, a scaled UAV is used to complete the balloon-borne launching test. The results show that the longitudinal control method can analyse the longitudinal aerodynamics and control characteristics accurately, and could be effectively utilized in the pull-up control of the balloon-borne solar powered UAV.

In this paper, we propose a frequentist model averaging method for composite quantile regression with diverging number of parameters. Different from the traditional model averaging for quantile regression which considers only a single quantile, our proposed model averaging estimator is based on multiple quantiles. The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights. The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error. Simulation studies are conducted to demonstrate the finite sample performance of our new model averaging estimator. The proposed method is also applied to the analysis of the stock returns data and the wage data.

Lithology classification using well logs plays a key role in reservoir exploration.This paper studies the problem of lithology identification based on the set-valued method (SV),which uses the SV model to establish the relation between logging data and lithologic types at a certain depth point.In particular,the system model is built on the assumption that the noise between logging data and lithologic types is normally distributed,and then the system parameters are estimated by SV method based on the existing identification criteria.The logging data of Shengli Oilfield in Jiyang Depression are used to verify the effectiveness of SV method.The results indicate that the SV model classifies lithology more accurately than the Logistic Regression model (LR) and more stably than uninterpretable models on imbalanced dataset.Specifically,the Macro-F1 of the SV models (i.e.,SV (3),SV (5),and SV (7)) are higher than 85%,where the sandstone samples account for only 22%.In addition,the SV (7) lithology identification system achieves the best stability,which is of great practical significance to reservoir exploration.

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.

In this paper, the formation control problem is investigated for a team of uncertain underactuated surface vessels (USVs) based on a directed graph. Considering the risk of collision and the limited communication range of USVs, the prescribed performance control (PPC) methodology is employed to ensure collision avoidance and connectivity maintenance. An event-triggered mechanism is designed to reasonably use the limited communication resources. Moreover, neural networks (NNs) and an auxiliary variable are constructed to deal with the problems of uncertain nonlinearities and underactuation, respectively. Then, an event-triggered formation control scheme is proposed to ensure that all signals of the closed-loop system are uniformly ultimately bounded (UUB). Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

The estimation of high dimensional covariance matrices is an interesting and important research topic for many empirical time series problems such as asset allocation. To solve this dimension dilemma, a factor structure has often been taken into account. This paper proposes a dynamic factor structure whose factor loadings are generated in reproducing kernel Hilbert space (RKHS), to capture the dynamic feature of the covariance matrix. A simulation study is carried out to demonstrate its performance. Four different conditional variance models are considered for checking the robustness of our method and solving the conditional heteroscedasticity in the empirical study. By exploring the performance among eight introduced model candidates and the market baseline, the empirical study from 2001 to 2017 shows that portfolio allocation based on this dynamic factor structure can significantly reduce the variance, i.e., the risk, of portfolio and thus outperform the market baseline and the ones based on the traditional factor model.

Previously, many studies have illustrated corner blend problem with different parameter curves. Only a few of them take a Pythagorean-hodograph (PH) curve as the transition arc, let alone corresponding real-time interpolation methods. In this paper, an integrated corner-transition mixing-interpolation-based scheme (ICMS) is proposed, considering transition error and machine tool kinematics. Firstly, the ICMS smooths the sharp corners in a linear path through blending the linear path with G3 continuous PH transition curves. To obtain optimal PH transition curves globally, the problem of corner smoothing is formulated as an optimization problem with constraints. In order to improve optimization efficiency, the transition error constraint is deduced analytically, so is the curvature extreme of each transition curve. After being blended with PH transition curves, a linear path has become a blend curve. Secondly, the ICMS adopts a novel mixed interpolator to process this kind of blend curves by considering machine tool kinematics. The mixed interpolator can not only implement jerk-limited feedrate scheduling with critical points detection, but also realize self-switching of two interpolation modes. Finally, two patterns are machined with a carving platform based on ICMS. Experimental results show the effectiveness of ICMS.

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.

PID (proportional-integral-derivative) control is recognized to be the most widely and successfully employed control strategy by far. However, there are limited theoretical investigations explaining the rationale why PID can work so well when dealing with nonlinear uncertain systems. This paper continues the previous researches towards establishing a theoretical foundation of PID control, by studying the regulation problem of PID control for nonaffine uncertain nonlinear stochastic systems. To be specific, a three dimensional parameter set will be constructed explicitly based on some prior knowledge on bounds of partial derivatives of both the drift and diffusion terms. It will be shown that the closed-loop control system will achieve exponential stability in the mean square sense under PID control, whenever the controller parameters are chosen from the constructed parameter set. Moreover, similar results can also be obtained for PD (PI) control in some special cases. A numerical example will be provided to illustrate 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,from the view of a defender,addresses the security problem of cyber-physical systems (CPSs) subject to stealthy false data injection (FDI) attacks that cannot be detected by a residual-based anomaly detector without other defensive measures.To detect such a class of FDI attacks,a stochastic coding scheme,which codes the sensor measurement with a Gaussian stochastic signal at the sensor side,is proposed to assist an anomaly detector to expose the FDI attack.In order to ensure the system performance in the normal operational context,a decoder is adopted to decode the coded sensor measurement when received at the controller side.With this detection scheme,the residual under the attack can be significantly different from that in the normal situation,and thus trigger an alarm.The design condition of the coding signal covariance is derived to meet the constraints of false alarm rate and attack detection rate.To minimize the trace of the coding signal covariance,the design problem of the coding signal is converted into a constraint non-convex optimization problem,and an estimation-optimization iteration algorithm is presented to obtain a numerical solution of the coding signal covariance.A numerical example is given to verify the effectiveness of the proposed scheme.

The optimal control problem with a long run average cost is investigated for unknown linear discrete-time systems with additive noise. The authors propose a value iteration-based stochastic adaptive dynamic programming (VI-based SADP) algorithm, based on which the optimal controller is obtained. Different from the existing relevant work, the algorithm does not need to estimate the expectation (conditional expectation) and variance (conditional variance) of states or other relevant variables, and the convergence of the algorithm can be proved rigorously. A simulation example is given to verify the effectiveness of the proposed approach.

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.

This work is intended to solve the least squares semidefinite program with a banded structure. A limited memory BFGS method is presented to solve this structured program of high dimension. In the algorithm, the inverse power iteration and orthogonal iteration are employed to calculate partial eigenvectors instead of full decomposition of n×n matrices. One key feature of the algorithm is that it is proved to be globally convergent under inexact gradient information. Preliminary numerical results indicate that the proposed algorithm is comparable with the inexact smoothing Newton method on some large instances of the structured problem.

In this paper, the $L_{2,\infty}$ normalization of the weight matrices is used to enhance the robustness and accuracy of the deep neural network (DNN) with Relu as activation functions. It is shown that the $L_{2,\infty}$ normalization leads to large dihedral angles between two adjacent faces of the DNN function graph and hence smoother DNN functions, which reduces over-fitting of the DNN. A global measure is proposed for the robustness of a classification DNN, which is the average radius of the maximal robust spheres with the training samples as centers. A lower bound for the robustness measure in terms of the $L_{2,\infty}$ norm is given. Finally, an upper bound for the Rademacher complexity of DNNs with $L_{2,\infty}$ normalization is given. An algorithm is given to train DNNs with the $L_{2,\infty}$ normalization and numerical experimental results are used to show that the $L_{2,\infty}$ normalization is effective in terms of improving the robustness and accuracy.

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.

This paper presents an active disturbance rejection control (ADRC) method for a class of second-order nonlinear uncertain systems with guaranteed transient and steady state tracking error bounds. To deal with the tracking error constraint, an output error transformation and sliding surface technique are introduced to transform the constrained second-order system into an equivalent unconstrained first-order one. Then, an ADRC method is developed to achieve output tracking of the transformed uncertain system. The author proves that the closed-loop system is semi-globally uniformly bounded and it is sufficient to guarantee the tracking error constraint for the original system. Simulation results of a system of two inverted pendulums connected by a spring and a damper demonstrate the effectiveness of the proposed control method.

This paper investigates the pinning synchronization of a group of coupled oscillators,where both the dissipative and restorative interactions are taken into consideration.The paired coupling topologies are introduced to capture this feature of the dynamics.To realize the synchronization of the coupled oscillators,the pinning control is introduced,and two pinning criteria are proposed to ensure the synchronization.Both these two proposed criteria provide sufficient and necessary conditions for pinning synchronization of the coupled oscillators with paired topologies.Simulation examples are illustrated to verify the proposed theoretical results.

This paper studies global robust tracking of uncertain Euler-Lagrange systems with input disturbances.The authors develop a robust regulation-based approach for the problem.Specifically,by introducing a novel nonlinear internal model,the authors solve global asymptotic trajectory tracking with disturbance rejection of multiple step/sinusoidal signals with unknown amplitudes,frequencies,and phases.Moreover,the authors show that a robustness property to actuator noises can be guaranteed in a sense of strong integral input-to-state stability (iISS).That is,the closed-loop system is not only iISS but also input-to-state stable (ISS) to small magnitude actuator noises.Furthermore,the authors explore a by-product overparametrized linear regression estimation,coming up with robust estimation of the unknown parameters.Finally,the authors present several numerical examples to illustrate the theoretical results.

Controllable canonical forms play important roles in the analysis and design of control systems. In this paper, a fundamental class of discrete-time bilinear systems are considered. Such systems are of interest since, on one hand, they have the most complete controllability theory. On the other hand, they can be nearly-controllable even if controllability fails. Firstly, controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived. Then, controllable canonical forms and nearly-controllable canonical forms of the systems are presented, respectively, where the corresponding transformation matrices are also explicitly constructed. Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.

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 focuses on the leader-following consensus control problem for nonlinear multiagent systems subject to deferred asymmetric time-varying state constraints. A distributed eventtriggered adaptive neural control approach is advanced. By virtue of a distributed sliding-mode estimator, the leader-following consensus control problem is converted into multiple simplified tracking control problems. Afterwards, a shifting function is utilized to transform the error variables such that the initial tracking condition can be totally unknown and the state constraints can be imposed at a specified time instant. Meanwhile, the deferred asymmetric time-varying full state constraints are addressed by a class of asymmetric barrier Lyapunov function. In order to reduce the burden of communication, a relative threshold event-triggered mechanism is incorporated into controller and Zeno behavior is excluded. Based on Lyapunov stability theorem, all closed-loop signals are proved to be semi-globally uniformly ultimately bounded. Finally, a practical simulation example is given to verify the presented control scheme.

By using Chen, Hou and Mu's extended Zeilberger algorithm, the authors obtain two recurrence relations for Callan's generalization of Narayana polynomials. Based on these recurrence relations, the authors further prove the real-rootedness and asymptotic normality of Callan's Narayana polynomials.

The purpose of this paper is two fold.First,the authors investigate quantile regression (QR) estimation for single-index QR models when the response is subject to random left truncation.The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed.The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained.Further,by combining the QR loss function and the adaptive LASSO penalization,a variable selection procedure for the index parameter is introduced and its oracle property is established.Second,a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square distribution.Furthermore,confidence regions of the index parameter can be constructed.The finite sample performance of the proposed methods are demonstrated.A real data analysis is also conducted to show the usefulness of the proposed approaches.

With the development of China's economy, environmental pollution has become cumulatively serious. The primary source of environmental pollution is thermal power generation, which has attracted the attention of governments and academia in recent years. To effectively reduce environmental pollution, research should study how to constrain the undesirable output of thermal power plants, that is, to limit the total undesirable output of the plants to a certain fixed sum. However, few studies have suggested that these undesirable outputs should be fixed-sum outputs. Moreover, no previous research publication about thermal power plants has analyzed their environmental performance changes. To address these gaps, a novel Malmquist-DEA approach is proposed for evaluate the environmental performance of thermal power plants in this paper. This approach generalizes the equilibrium efficient frontier DEA model with fixed-sum undesirable outputs and incorporates the model into the Malmquist productivity index (MPI). The authors apply this approach to the analysis of provincial thermal power plant environmental performance in China and analyze such plants' trends based on panel data from 2011 to 2014. The empirical research shows that the environmental performance of regional thermal power plants was positively affected by efficiency change and negatively affected by technical change. Finally, the authors provide policy suggestions based on our findings.

This paper investigates the containment problem of continuous-time multi-agent systems with multiplicative noises, where the first-order and second-order multi-agent systems are studied respectively. Based on stochastic analysis tools, algebraic graph theory, and Lyapunov function method, the containment protocols based the relative states measurement with multiplicative noises are developed to guarantee the mean square and almost sure containment. Moreover, the sufficient conditions and necessary conditions related to the control gains are derived for achieving mean square and almost sure containment. It is also shown that multiplicative noises may works positively for the almost sure containment of the first-order multi-agent systems. Simulation examples are also introduced to illustrate the effectiveness of the theoretical results.

The key issue in the frequentist model averaging is the choice of weights.In this paper,the authors advocate an asymptotic framework of mean-squared prediction error (MSPE) and develop a model averaging criterion for multistep prediction in an infinite order autoregressive (AR (∞)) process.Under the assumption that the order of the candidate model is bounded,this criterion is proved to be asymptotically optimal,in the sense of achieving the lowest out of sample MSPE for the samerealization prediction.Simulations and real data analysis further demonstrate the effectiveness and the efficiency of the theoretical results.

This paper designs a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, the authors aim to find a generalized Nash equilibrium in the worst case. However, it is challenging to obtain the exact equilibria directly because the parameters are from general convex sets, which may not have analytic expressions or are endowed with high-dimensional nonlinearities. To solve this problem, the authors first approximate parameter sets with inscribed polyhedrons, and transform the approximate problem in the worst case into an extended certain game with resource allocation constraints by robust optimization. Then the authors propose a distributed algorithm for this certain game and prove that an equilibrium obtained from the algorithm induces an ε-generalized Nash equilibrium of the original game, followed by convergence analysis. Moreover, resorting to the metric spaces and the analysis on nonlinear perturbed systems, the authors estimate the approximation accuracy related to ε and point out the factors influencing the accuracy of ε.

This paper investigates the equivalence problem of bivariate polynomial matrices. A necessary and sufficient condition for the equivalence of a square matrix with the determinant being some power of a univariate irreducible polynomial and its Smith form is proposed. Meanwhile, the authors present an algorithm that reduces this class of bivariate polynomial matrices to their Smith forms, and an example is given to illustrate the effectiveness of the algorithm. In addition, the authors generalize the main result to the non-square case.

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 considers the stabilization of the coupled wave systems with spatially-varying coefficients. The authors design a state feedback controller by backstepping method. In contrast to the previous work in the literature, the kernel equations become more complicated and the main difficulty lies in proving the existence and uniqueness of the solution to the kernel equations. Firstly, using the backstepping approach, the authors verify the kernel equations, which is a system of coupled hyperbolic equations with spatially-varying coefficients. Then, the existence and uniqueness of the kernel matrices is obtained. Finally, the authors use a Lyapunov function to get the exponential stabilization of the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed controller.

In this study,an adaptive asymptotic tracking control problem is considered for stochastic nonlinear systems with unknown backlash-like hysteresis.By utilizing backstepping technology and bound estimation approach,an adaptive asymptotic tracking control scheme is designed,where fuzzy systems are applied to approximate unknown function terms,the effect of hysteresis and stochastic disturbances is compensated appropriately.The proposed scheme ensures that the tracking error can asymptotically converge to zero in probability and all signals of the closed-loop system are bounded almost surely.Finally,the effectiveness of the control scheme is verified by giving a simulation example.

Chinese Reminder Theorem (CRT) for integers has been widely used to construct secret sharing schemes for different scenarios, but these schemes have lower information rates than that of Lagrange interpolation-based schemes. In ASIACRYPT 2018, Ning, et al. constructed a perfect $(r,n)$-threshold scheme based on CRT for polynomial ring over finite field, and the corresponding information rate is one which is the greatest case for a $(r,n)$-threshold scheme. However, for many practical purposes, the information rate of Ning, et al. scheme is low and perfect security is too much security. In this work, the authors generalize the Ning, et al. $(r,n)$-threshold scheme to a $(t,r,n)$-ramp scheme based on CRT for polynomial ring over finite field, which attains the greatest information rate $(r-t)$ for a $(t,r,n)$-ramp scheme. Moreover, for any given $2\leq r_1 < r_2\leq n$, the ramp scheme can be used to construct a $(r_1,n)$-threshold scheme that is threshold changeable to $(r',n)$-threshold scheme for all $r'\in \{r_1+1,r_1+2,\cdots,r_2\}$. The threshold changeable secret sharing (TCSS) scheme has a greater information rate than other existing TCSS schemes of this type.

The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments. The generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial design. In this paper, we give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower bound. These methods are all deterministic construction methods which can avoid the complexity of stochastic algorithms. Both saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these methods. Moreover, the resulting designs are also χ²-optimal and minimum moment aberration designs.

This paper investigates the state consensus of linear multi-agent systems in a graph where each agent is equipped with two novel event-triggering mechanisms. Each agent utilizes them to avoid continuous information transmissions with its neighbors and to reduce the frequencies of controller updates, respectively. One of the event-triggering mechanisms defines a threshold of state errors by a constant plus a state-dependent variable. The other event-triggering mechanism introduces a period of rest time after each event. For each agent, both event-triggering mechanisms are fully distributed and are independent of any global information. The authors utilize a co-design approach to deal with the interplay between control gains and parameters in event-triggering mechanisms. With appropriate control gains in control laws and parameters in event-triggering conditions, subsystems employing discrete-time signals from neighbors and discrete-time signals from their controllers achieve the state consensus. Simulations are performed to illustrate the effectiveness of the proposed event-triggering mechanisms.

This paper considers a distributed nonsmooth resource allocation problem of minimizing a global convex function formed by a sum of local nonsmooth convex functions with coupled constraints. A distributed communication-efficient mirror-descent algorithm, which can reduce communication rounds between agents over the network, is designed for the distributed resource allocation problem. By employing communication-sliding methods, agents can find a ε-solution in O($\frac{1}{\varepsilon }$) communication rounds while maintaining O($\frac{1}{\varepsilon ^2}$) subgradient evaluations for nonsmooth convex functions. A numerical example is also given to illustrate the effectiveness of the proposed algorithm.

Business survey,which starts from the microeconomic level,is a widely used short-term forecasting tool in practice.In this study,the authors examine whether foreign trade survey data collected by China's Ministry of Commerce would provide reliable forecasts of China's foreign trade.The research procedure is designed from three perspectives including forecast information test,turning point forecast,and out-of-sample value forecast.First,Granger causality test detects whether survey data lead exports and imports.Second,business cycle analysis,a non-model based method,is performed.The authors construct composite indexes with business survey data to forecast turning points of foreign trade.Third,model-based numerical forecasting methods,including the Autoregressive Integrated Moving Average Model with Exogenous Variables (ARIMAX) and the artificial neural networks (ANNs) models are estimated.Empirical results show that survey data granger cause imports and exports,the leading composite index provides signal for changes of trade cycles,and quantitative models including survey data generate more accurate forecasts than benchmark models.It is concluded that trade survey data has excellent predictive capabilities for imports and exports,which can offer some priorities for government policy-making and enterprise decision making.