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A NEW CONSTRAINTS IDENTIFICATION TECHNIQUE-BASED QP-FREE ALGORITHM FOR THE SOLUTION OF INEQUALITY CONSTRAINED MINIMIZATION PROBLEMS

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Journal of Computational Mathematics 2006年第5期24卷 591-608页

作者： Chang-yin Zhou Guo-ping He Yong-li Wang Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 China college of information science and Engineering Shandong University of Science and Technology Qingdao 266510 China college of information science and Engineering Shandong University of Science and Technology Qingdao 266510 China

In this paper, we propose a feasible QP-free method for solving nonlinear inequality constrained optimization problems. A new working set is proposed to estimate the active set. Specially, to determine the working set, the new method makes use of the multiplier information from the previous iteration, eliminating the need to compute a multiplier function. At each iteration, two or three reduced symmetric systems of linear equations with a common coefficient matrix involving only constraints in the working set are solved, and when the iterate is sufficiently close to a KKT point, only two of them are involved. Moreover, the new algorithm is proved to be globally convergent to a KKT point under mild conditions. Without assuming the strict complementarity, the convergence rate is superlinear under a condition weaker than the strong second-order sufficiency condition. Numerical experiments illustrate the efficiency of the algorithm.

关键词： QP-free method Optimization Global convergence Superlinear convergence,Constraints identification technique.

H_∞ CONTROL FOR STOCHASTIC SYSTEMS WITH POISSON JUMPS

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Journal of Systems science & Complexity 2011年第4期24卷 683-700页

作者： Xiangyun LIN Rui ZHANG Schooi of Mathematics Shandong University Jinan 250100 China college of science Shandong Universityof Science and Technology Qingdao 266510 China. college of information science and technology Shandong University of Science and Technology Qingdao 266510 China.

This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H∞ control design is also extended to such systems.

关键词： Externally stable H∞ control internally stable Poisson random measure Riccati equa-tion stochastic system with jumps.

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

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Communications in Theoretical Physics 2008年第12期50卷 1269-1275页

作者： XU Xi-Xiang YANG Hong-Xiang LU Rong-Wu college of science Shandong University of Science and Technology Qingdao 266510 China Department of information science and technology Taishan College Tai＇an 271021 China

A semi-direct sum of two Lie algebras of four-by-four matrices is presented,and a discrete four-by-fourmatrix spectral problem is introduced.A hierarchy of discrete integrable coupling systems is *** obtainedintegrable coupling systems are all written in their Hamiltonian forms by the discrete variational ***,we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discreteHamiltonian systems.

关键词： integrable lattice equation semi-direct sum of Lie algebra integrable coupling system discrete variational identity Hamiltonian form Liouville integrability

Approximately optimal tracking control for discrete time-delay systems with disturbances

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Progress in Natural science:Materials International 2008年第2期18卷 225-231页

作者： Gongyou Tang a,,Huiying Sun b,Haiping Pang c a college of information science and Engineering,Ocean university of China,qingdao 266100,China b college of information and Electrical Engineering,Shandong university of science and technology,qingdao 266510,China c college of Automation and Electronic Engineering,qingdao university of science and technology,qingdao 266042,China college of information science and Engineering Ocean University of China Qingdao 266100 China college of information and Electrical Engineering Shandong University of Science and Technology Qingdao 266510 China college of Automation and Electronic Engineering Qingdao University of Science and Technology Qingdao 266042 China

Optimal tracking control (OTC) for discrete time-delay systems affected by persistent disturbances with quadratic performance index is considered. By introducing a sensitivity parameter,the original OTC problem is transformed into a series of two-point boundary value (TPBV) problems without time-advance or time-delay terms. The obtained OTC law consists of analytic feedforward and feedback terms and a compensation term which is the sum of an infinite series of adjoint vectors. The analytic feedforward and feedback terms can be found by solving a Riccati matrix equation and two Stein matrix equations. The compensation term can be obtained by using an iteration formula of the adjoint vectors. Observers are constructed to make the approximate OTC law physically realizable. A simulation example shows that the approximate approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.

关键词： Discrete systems Time-delay systems Disturbances Optimal control Tracking control

THE DYNAMICS AND THERAPEUTIC STRATEGIES OF A SEIS EPIDEMIC MODEL

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International Journal of Biomathematics 2013年第5期6卷 41-58页

作者： XINZHU MENG ZHITAO WU TONGQIAN ZHANG college of information science and engineeringshandong university of science and technology qingdao 266590 P. R. China college of science Shandong University of Science and Technology Qingdao 266590 P. R. China

Based on an epidemic model which Manvendra and Vinay [Mathematical model to simulate infections disease, VSRD-TNTJ 3（2）（2012） 60 68] have proposed, we consider the dynamics and therapeutic strategy of a SEIS epidemic model with latent patients and active patients. First, the basic reproduction number is established by applying the method of the next generation matrix. By means of appropriate Lyapunov functions, it is proven that while the basic reproduction number 0 〈 R0 〈 1, the disease-free equilibrium is globally asymptotically stable and the disease eliminates; and if the basic reproduction number R0 〉 1, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic. Numerical investigations of their basin of attraction indicate that the locally stable equilibria are global attractors. Second, we consider the impact of treatment on epidemic disease and analytically determine the most effective therapeutic strategy. We conclude that the most effective therapeutic strategy consists of treating both the exposed and the infectious, while treating only the exposed is the least effective therapeutic strategy. Finally, numerical simulations are given to illustrate the effectiveness of the proposed results.

关键词： Endemic disease bilinear incidence local stability global stability treatmentstrategies.

New Matrix Loop Algebra and Its Application

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Communications in Theoretical Physics 2008年第8期50卷 321-325页

作者： DONG Huan-He XU Yue-Cai college of information science and Engineering Shandong University of Science and Technology Qingdao 266510 China college of Continuing Education Shangdong University of Science and Technology Taian 271000 China

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of the above system is ***,the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.

关键词： matrix loop algebra Liouville integrable system Hamiltonian structure integrable couplings

Infinite horizon linear quadratic differential games for discrete-time stochastic systems

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控制理论与应用（英文版） 2012年第3期10卷 391-396页

作者： Huiying SUN Liuyang JIANG Weihai ZHANG college of information and Electrical Engineering Shandong University of Science and TechnologyQingdao Shandong 266510China

This paper deals with the infinite horizon linear quadratic （LQ） differential games for discrete-time stochas- tic systems with both state and control dependent noise. The Popov-Belevitch-Hautus （PBH） criteria for exact observability and exact detectability of discrete-time stochastic systems are presented. By means of them, we give the optimal strategies （Nash equilibrium strategies） and the optimal cost values for infinite horizon stochastic differential games. It indicates that the infinite horizon LQ stochastic differential gaines are associated with four coupled matrix-valued equations. Further- more, an iterative algorithm is proposed to solve the four coupled equations. Finally, an example is given to demonstrate our results.

关键词： Discrete-time stochastic systems Exact observability Exact detectability Differential games Nash equi-librium

ANALYSIS FOR GENE NETWORKS BASED ON LOGIC RELATIONSHIPS

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Journal of Systems science & Complexity 2010年第5期23卷 999-1011页

作者： Shudong WANG Yan CHEN Qingyun WANG Eryan LI Yansen SU Dazhi MENG college of information science and Engineering Shandong University of Science and Technology Qingdao 266510 China college of Applied sciences Beijing University of Technology Beijing 100124 China college of Mathematics and Computer science GanNan Normal University GanZhou 341000 China

The reverse construction and analysis of the networks of molecular interactions are essential for understanding their functions within cells. In this paper, a logic network model is constructed to investigate the complicated regulation mechanism of shoot genes of Arabidopsis Thaliana in response to stimuli. The dynamics of the complicated logic network is analyzed, discussed, and simulated. The simulation results show that the logic network of the active genes of shoot eventually evolves into eleven attractors under the stimuli, including five 1-periodic and six 2-periodic attractors. Our work provides valuable reference and guidance for biologists to understand and explain Arabidopsis＇ response to external stimuli by experiments.

关键词： Dynamics gene network logic analysis of Phylogenetic profiles systems biology.

Set (k, n)-Exactly covering problem

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High technology Letters 2010年第4期16卷 433-436页

作者：吴振寰 Gao Ying Wu Zhehui college of information science ＆ Engineering Shandong University of Science ＆ Technology Qingdao 266510 P.R. China

With the （ k, n ）-threshold scheme of secret sharing in the field of information security technology as an application background, the concept of set （ k, n ）-exact cover is presented in this paper. It is a modification of the original concept of set covering problem. It is also different from the concept of exact cover defined by J.E. Hopcmft. Some properties of （k, n ） -exact cover are investigated; a sufficient condition for a set to be （ k, n ） -exactly coverable is given. It follows that a feasible assignment scheme of a set for the （ k, n） -exact eover is obtained if this set satisfies the sufficient condition.

关键词： set ( k n) -exact cover exactly covering match feasible assignment