In this paper, we consider the empirical Bayes (EB) one-sided and two-sided test problems for the parameter of Burr Type XII distribution. The EB test
rules are constructed by using the recursive kernel estimation of probability density function. The asymptotically optimal property and convergence rates for the proposed EB test rules are obtained under suitable conditions. Finally, an example shows the effectiveness of the main results.

We propose a sojourn-probability-dependent method to investigate $H_\infty$ filtering design for a class of discrete switched systems with time varying delay. A new type of switched system model and filter model is built by using the sojourn probability information. The sufficient condition of $H_\infty$ mean square stability for switched systems is given via Lyapunov functional method. Then robust $H_\infty$ filtering gains are derived. A numerical example is given to demonstrate the effectiveness and applicability of the proposed method.

Engineering cybernetics is not just about control, but more so about the interplay between information and control. Our understanding of the basic concepts such as feedback and disturbance deepens with a critical reflection on how critical information is recognized and obtained in the context of control design, so does our understanding of the past inventions and design principles. Prof. Jingqing Han, a pioneer, initiated the debate with an article in this journal 27 years ago. Sharing deep concerns regarding the premise on the accurate mathematical model in control theory with Prof. H.S. Tsien, who raised the problem of disturbance and uncertainties in control, Prof. Han made the crucial leap from the model-based design to the information-based design. The ensuing dualistic paradigm of controller-rejector design, with active disturbance rejection control as but one embodiment, provides both a framework and a new technological basis for the renewal and standardization of general purpose industrial control technologies, as well as a path back to the original vision of engineering cybernetics from Prof. Tsien. From the south-pointing chariot\\ to engineering cybernetics, from PID to active disturbance rejection control, from humanity to science and technology, from east to west, an information-centric conceptualization of control has persisted over centuries and is coming to fruition.

We discuss in this paper,the existence problem of periodic solutions of a nonautonomousHamiltonian system,J\dot{z}=G′_z(t,z).(*)We modify the corresponding variational functional with several factors,construct some spe-cial minimax value series and give the sharp estimates of their growth orders.Then we provethat the equation (*) possesses infinitely many periodic solutions when G(t,z)=H(z)+F(t,z) with H′_z(z) being sublinear at z=0 and with F′_z(t,z) being superlinear,and thattheir indices satisfy a certain relation.

The purpose of this article is to establish new simple approximative algorithms of fixed point for nonexpansive mappings and to prove new fixed point theorems for nonexpansive mappings in the reflexive Banach spaces. The approximate algorithms presented in this article are simpler than Mann, Ishikawa and Halpern iterative algorithms. The weak and strong convergence theorems are proved respectively. The new fixed point theorems presented here improve and extend the related results of Goebel-Kirk, Kim-Xu and others in some respects.

For the multi-sensor  descriptor system with correlated measurement noises,the new fused measurement can be obtained by  least square method based on  all measurements. The state equation of the descriptor system can be decomposed into two normal mutual coupling sub-systems by using
  singular value decomposition.  And  the fused  measurement equation  is changed to the measurement of one state component.  Then,   the problem is the state estimation of one-sensor normal system. For the new reduced-order sub-systems,  the weighted measurement fusion  Kalman predictor is presented, by applying   Kalman filtering.    The prediction error variances of the weighted measurement fusion Kalman  predictor for the descriptor system is obtained. This method avoids to compute the cross-variance of  all local predictors, and the accuracy   of fused predictor is higher than that of  local predictors and  state     fusion Kalman predictor. A simulation example of 4-sensor descriptor  system verifies the effectiveness of the method.

For a class of nonlinear systems with structural uncertainties and external disturbances, the robust $H_\infty$ control problem is investigated. By the method of Hamilton-Jaccobi inequality, a new robust $H_\infty$ performance criterion is derived, based on which, a state-feedback controller is designed. Furthermore, it is proved that results of this paper are completely consistent with the classical ones for linear systems. At last, simulation results are provided to demonstrate the effectiveness of the present results.

In this paper, we will give an overview on the status of the research on the nonlinear output regulation problem with the emphasis on the establishment of a nonlinear version of the internal model principle and its role in shaping a general framework for handling the nonlinear output regulation problem.

In this paper, the synthetic function for the time optimal control of the second-order discretetime system is obtained by the Isochronic Region method. Based on this function, the discrete form of tracking-differentiator is constructed. Numerical simulation shows that this discrete form of tracking-differentiator can quickly trck an input signal without overshoot and chattering and can produce a good differential signal.

In this paper we prove that if the polar cone Λ* of a closed convex cone Λis sharp or is generated by a closed ball not containing θ, then Λ is solid. We also prove thatquasi--polyhedron cones and cones with non-empty weak-star interior of p

The paper first gives a comprehensive comparison of the frame of the Active Disturbance Rejection Control (AQDRC) with other methods for controlling uncertain systems, which includes the adaptive control, robust control, disturbance observers based methods, etc. Then the process of theoretical analysis for ADRC, mainly concluding the convergence of the tracking differentiator (TD), the capabilities of the extended state observer (ESO) for estimating
uncertainties and the performance of the ADRC based closed-loop system is reviewed. Finally, ADRC's contributions to the research of controlling uncertain systems are concluded.

Biomimetic robotic fish, as one kind of highly efficient and highly maneuverable underwater robots, achieved the widespread concern of researchers. In this paper, the major research developments in propulsion mechanism and system development of biomimetic robotic fish were presented. Through the analysis, the main issues of biomimetic robotic fish were summarized and the research ideas of propulsion mechanism, mechanism optimization and
motion control were also emphatically discussed.

In this paper the concept of ``self-clustering" is presented. It is one kind of the self-organizing and widely existing in complex systems. For the function of complex systems, there is a well-known inequality $1+1>2$ , showing that the whole is more than the sum of its parts. Could it seek one more quantitative expression for the function of complex systems? For this purpose a simple but widely representative network model is given. With this model, the process of growing, evolving and emergence of the system can be analyzed and a quantitative/qualitative expression $f(n)=\frac{1}{2}n(n-1)$ for system function can be derived. This expression indicates properties of the system function and gives explanations of some important phenomena.  Such as: $1+1>2$ is a special case of $f(n)$ as $n=2$. Moreover, $f(n)$ shows the nonlinearity obviously.  It also shows that at the initial stage of the process, adding or losing a few components will give rise to notable effect to the system function.  There will be a steady emergence as $n$ increased to a considerable amount.
  Thus, it reveals the change that from the fragility at the initial stage to the robustness accompanying the steady emergence.  In addition, $f(n)$ implies positive feedback.  An expression is given to show this mechanism, which turns out to be the mechanism of "increasing returns" and the mechanism of ``preferential attachment",  leading to the scale-free network structure. Finally, a brief conclusion regarding complexity and simplicity is given.

This paper is concerned with an initial-boundary problem of nonconvex scalar conservation laws with two pieces of constant initial data and
constant boundary data. Under the condition that the flux function has one inflection point, by the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method for the global weak entropy solution of the initial-boundary value problem and clarify the solution structure nearby the boundary. In contrast to the initial-boundary value problem for strictly convex
scalar conservation laws, the weak entropy solution of the initial-boundary value problem for nonconvex scalar conservation laws includes the following new interaction type: a contact or non-contact shock collides with the boundary and a new non-contact shock wave rebounds from the boundary.

Interest rate is one of the important indicators for banks and other financial institutions to balance the risks  and gains.  In this paper, based on the  decision-making behavior of the borrower,  a model for interest rate decision based  on the conditional value-at-risk (CVaR) is established,  and   the optimal interest rate is obtained.  Numerical analysis shows that  the level of risk aversion directly effects interest rate decision;  CVaR could help banks to balance profit and risk; borrowers'  profit rate and internal capital are the key factors for bank evading risk.

In this paper, a third-order three-point boundary value problem with \emph{p}-Laplacian is considered. By using Avery-Peterson fixed point theorem, it is proven that there exist at least three positive solutions for the above problem, when $f$ satisfies some growth conditions.

The theoretical research and practical applications  of complex nonlinear systems and control have drawn more and more ttention following the development of modern science and technologyin various branches of scientific and social areas.  In view of theresearch difficulties and significance in the studies of complexnonlinear systems and control, the paper investigates three key  problems, including nonsmooth systems and control, networked systems
and control, and analysis and control of criticality.  On the one and, the paper is a brief summary of some of our obtained research results in the related areas. On the other hand, it can also be  viewed as a note to show our gratitude and congratulations to the 50th anniversary of Technical Committee of Control Theory of Chinese Association of Automation.

Improving the performance of optimization algorithms has long been an important pursuit of researchers. It is a typical design idea and paradigm to combine different optimizers for a synergy of their complementary advantages. Regarding two kinds of population-based evolutionary algorithms, the particle swarm optimizer (PSO) and the differential evolution (DE), we present a systematic and comprehensive survey on their hybrids (DEPSOs) in the literature and propose a taxonomy of hybridization strategies.  Based on the taxonomy, we make a classification of different DEPSOs and analyze their similarities and differences.  We also point out some new directions for future research and provide several guidelines for hybridization design of optimizers.

In unreplicated factorial experiments, if the dispersion effects of factors $A, B$ are active, the existing estimators of dispersion effects are often biased whether or not the dispersion effect of interaction factor $AB$ is active. This results  in $AB$ be spuriously identified active factor. In this paper, we propose a new estimator of dispersion effects (called the ML estimator), and give the exact expression of the variance of ML estimator. We prove that the ML
estimator of dispersion effect of interaction factor $AB$ is unbiased in a class of models. Finally, a comparison is given between the ML estimator and the existing and commonly used estimators.

In this paper,we point out that Hilbert's Mechanization Theorem may be extended to allconstructible theorems which can be mechanically proved in the same way by adjoining somenew constructive types.Using the Theorem-Prover built by the authors in rearranging thesteps of Wu's algorithm,many non-trivial theorems have been proved and some new resultshave also been discovered independently.

This paper is concerned with the practical  tracking control of nonlinear feedforward systems by  using the homogeneous systems theory,  and a
 homogeneous domination approach is proposed to solve the tracking problem. The nonlinear systems in this paper are high-order and the
 unmeasurable states are of the form of high-order growth. The proposed controller does not depend on the  reference signals, and so that the error is small enough. Finally, the simulations illustrate the effectiveness of the result.

Since many discrete production processes can be described by using discretevent systems, discrete event dynamic systems have a very strong background of applications,for instance, application to flexible manufacturing systems. So great attention has been paid to discrete-event dynamic systems both domestically and internationally, deep studies were made,and a number of meaningful results were obtained. In this paper we try to give explanatory notes and new proofs for some important results by using the graph theory viewpoint and methods,and attempt to go further into the application of graph theory to the study of discrete-event dynamic systems.

This paper presents a zero decomposition theorem and algorithm based on Wu's method, which computes a zero decomposition with invarint multiplicity for a given zero-dimensional polynomial system. It is shown that the zero decomposition is of triangular form if the system satisfies some assumption.

The two-echelon supply chain under stochastic manufacturing demand has
a single component supplier selling to a single manufacturer. The model with perpetual manufacturing demand and many replenishment opportunities is considered by analytic method. The problem can be modeled as a supplier-led Stackelberg dynamic game. Supply chain performances under consignment and non-consignment are considered respectively. The supplier, acting as a designer
of supply chain, offers the manufacturer a backorder penalty cost share allocation, and then the manufacturer decides the optimal base stock level. In this paper the following conclusions are obtained. Under consignment, there is a unique equilibrium solution in the game, and the supply chain system is optimal. Under non-consignment, there is a unique equilibrium solution in the game, and the supply chain system is optimal. Supply chain performance under consignment is superior to that under non-consignment.

A method of LMI, a kind of Lyapunov-Krasovskii functional, which is based on ``descriptor form", and a new type of memory state feedback controller are used to solve the problem of $H^{\infty}$ controller, designing new adaptive strategies for two unknown constant: input delay and up bound for norm of the uncertain nonlinear part. This type of strategy isn't limited in the estimate value as that of the old adaptive controllers and manages to avoid calculating ``adjusting constant", which guarantees the limitation as the old adaptive
controllers, by reflecting difference between the estimate value and the value being close to the practical. The sufficient condition of its solution is given with a numerical example.

Observing the development of the control theory one sees that there are basically two diff-erent approaches:Model Analysis and Direct Control Approach.In the past three decades themodel analysis approach has been the dominating one,while the classical regulation theory andthe guidance theory,etc.are of Direct Control Approach.There is no clear line between the linearity and non-linearity in control systems.The pur-pose of the control is,more or less,a kind of time-varying process of optimization;it is not aglobal system optimization.The value of feedback is not necessarily a function of state variables;it may be some time-varying quantity.To solve the problems of robustness and adaptability of control systems,it is necessary toget rid of the mathematical model of the systems,and to find the control law,which does notdepend on particular expressions of the system.

In this papers we discuss the problem of getting continuous signal and differential signal properly from the singal which is not differentiable. We give the generalform and some kinds of concrete realization of nonlinear Tracking-Differentiatorwhich can solve the problem stated above. Lastly, we do a simulation research onthe concrete realization.

A new method for searching for the solution to the least square estimation withlinear inequality constraints is proposed on the basis of sufficient or necessary con-ditions of the solution given in this paper.Compared with enumeration the newapproach can significantly decrese calculation.Finally the applicability of the sug-gested method is illustrated with a numerical example.

in this paper, we introduce a new concept, the strictly efficient point, in vector optimization in Banach spaces. This concept is shown to have many desirable properties and to be an extension of the super efficient point in Borwein's sense. Par

In this paper, we establish a model where fish feeded on algae on the base of the non-traditional biomanipulation method. We consider the effect of lake temperature in the model because greenhouse effect has become increasingly prominent due to the climate change,and the growth of fish and algae are all related to temperature of lake water. We analyze the existence and stability of the equilibrium. The threshold for algae and fish extinction are obtained  espectively, the implication of these results are discussed.

The regular exponential family(REF),that is,the natural exponential family with mini-murn-dimension and with the mean function m=Eex taken as a new parameter is discussed inthis paper.The importance of the REF with polynomial variance function (PVF-REF) ispointed out.When m is a single factor of PVF and the left-end of its defined domain is zero,thecorresponding REF is given as the single-side lattice distribution family.Other PVF-REF canbe obtained from a limit process.As an illustration,the results for all seven cases of P(3)VF aregiven.

The problem of exact solutions for Maccari system in stochastic environment is studied. By using Hermite transform in Kondratiev distribution space $({\mathcal {S}})_{-1}$ and the generalized $F$ expansion method, the Wick versions of white noise functional solutions for the Wick-type stochastic Maccari system and exact solutions for variable cofficient Maccari system are obtained.

This paper discusses the problem that $n$ jobs with their own deadlines have to be processed on  identical machines considering the idle insert. The objective is to find a preemptive job sequence so  as to minimize the total earliness. The complexity is considered firstly,  and the problem is proved
  strongly NP-hard through the induction of 3-partition problem. Then,  the special case of common deadline  is discussed. Since tardy jobs are prohibited,  it's possible that there is no feasible sequence for the  problem. The feasibility is considered primarily. If the problem is feasible,  a polynomial time algorithm
     is developed to achieve optimality.

Identification of several classes of stochastic nonlinear systems, i.e., the Wiener system, the Hammerstein system and the nonlinear ARX system, is considered. First, existing recursive and nonrecursive algorithms for identifying these systems are briefly summarized. Then, a unified framework to recursively identify these systems is introduced. Based on the Markov chains and mixing properties connected with these systems, the identification is transformed into root searching problems. Finally, identification algorithms based on stochastic approximation with expanding truncations are introduced
and strong consistency of estimates is established. The theoretical results are verified by simulation examples.

By combining the single-factor model and the multi-period mean-variance model, we first propose a new multi-period mean-variance model
under the single-factor model, and obtain its explicit optimal investment strategy by using the quadratic programming technique. As a generalization of
these conclusions, we then extend the above model to the multi-factor model situation and derive similar conclusions. Finally, some numerical examples show the effectiveness of the theoretical results.  

An adaptive neural network controller is presented for a class of strict-feedback nonlinear time-delay systems with unknown nonlinear functions. A radial basis function neural network is chosen to approximate the unknown nonlinear functions in this paper. The developed control scheme is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop systems.
The tracking error is proven to converge to a small compact set. A simulation example illustrates the effectiveness of the proposed approach.

This paper shows that the transmission zeros play an important role in a system withoutsteady errors and with structurally stable properties without steady errors.From the point ofview of the frequency domain,all our discussions are based on the Smith-McMillan form oflinear multivariable systems.The engineering sense of the“internal model principle”is revealedthrough the study of transmission zeros of the systems.The main results demonstrate that alinear multivariable time-invariant system possesses structurally stable properties without steadyerrors iff every numerator polynomialε_i(s)(i=1,2,…,min(r,m))of Smith-McMillanform of the closed loop transfer function matrix from f(s)to e(s)can be divided by α_1(s),the greatest invariant factor of N(S).The property thatε_i(s)can be divided by α_1(s)isstructurally stable.