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Series-based approximate approach of optimal tracking control for nonlinear systems with time-delay

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Progress in Natural science:Materials International 2008年第12期18卷 1571-1576页

作者： Gongyou Tang~a Mingqu Fan~(a,b) a college of information science and Engineering,Ocean university of china,Qingdao 266100,china b college of information and Engineering,Shandong university of science and Technology,Jinan 250031,china college of information science and Engineering Ocean University of China Qingdao 266100 China college of information and Engineering Shandong University of Science and Technology Jinan 250031 China

The optimal output tracking control (OTC) problem for nonlinear systems with time-delay is *** a series-based approx- imate approach,the original OTC problem is transformed into iteration solving linear two-point boundary value problems without time- *** OTC law obtained consists of analytical linear feedback and feedforward terms and a nonlinear compensation term with an infinite series of the adjoint *** truncating a finite sum of the adjoint vector series,an approximate optimal tracking control law is obtained.A reduced-order reference input observer is constructed to make the feedforward term physically *** exam- ples are used to test the validity of the series-based approximate approach.

关键词： Nonlinear systems Time-delay Tracking control Optimal control Observer

OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIAL EQUATIONS IN THE ABSENCE OF CONVEXITY

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Journal of Systems science & Complexity 2010年第2期23卷 321-333页

作者： Shu LUAN Hang GAO School of mathematics and Computation science Zhanjiang Normal College Zhanjiang 524048 China. School of mathematics and Statistics Northeast Normal University Changchun 130024 China.

In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of *** overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are *** the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is *** the end of this paper,the authors discuss the applicationof the maximum principle by an example.

关键词： Multisolution ODEs optimal control Pontryagin's maximum principle relaxed controls.

THE CONVERGENCE OF A NEW MODIFIED BFGS METHOD WITHOUT LINE SEARCHES FOR UNCONSTRAINED OPTIMIZATION OR COMPLEXITY SYSTEMS

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Journal of Systems science & Complexity 2010年第4期23卷 861-872页

作者： Liying LIU Zengxin WEI Xiaoping WU college of mathematics science Liaocheng University Liaocheng 252059 China college of mathematics and information science Guangxi University Nanning 530004 China School of Management Xi'an Jiaotong University Xi'an 710049 China

In this paper,a new modified BFGS method without line searches is *** traditionalBFGS method,this modified BFGS method is proposed based on the so-called fixed steplengthstrategy introduced by Sun and *** some suitable assumptions,the global convergence andthe superlinear convergence of the new algorithm are established,*** some preliminarynumerical experiments,which shows that the new Algorithm is feasible,is also reported.

关键词： BFGS method complexity systems global convergence superlinear convergence unconstrained optimization.

On quasi-convex mappings of order α in the unit ball of a complex Banach space

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science china mathematics 2006年第11期49卷 1451-1457页

作者： LIU Taishun & XU Qinghua Department of mathematics, Huzhou Teachers college, Huzhou, 313000, china Department of mathematics, Jiangxi normal university, Nanchang, 330022, china Department of mathematics Huzhou Teachers College Huzhou China Department of mathematics Jiangxi Normal University Nanchang China

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.

关键词： coefficient estimation the homogeneous expansion quasi-convex mapping quasi-convex mapping of order a.

Transition of Growth Mode in Homoepitaxy on Metal Surface

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Communications in Theoretical Physics 2007年第7期48卷 175-178页

作者： WU Li-Li LU Hang-Jun WU Feng-Min college of mathematics and Physics,information Engineering,Zhejiang normal university,Jinhua 321004,china college of mathematics and Physics Information Engineering Zhejiang Normal University Jinhua 321004 China

The process of the multilayer growth of Pt on Pt(111)is studied by using a Monte Carlo model with realisticphysical *** effects of the substrate temperature,the ES barrier,and the deposition rate on the growthmode have been *** transitions of the surface roughness from oscillatory to non-oscillatory behaviorand then back to oscillatory behavior are observed while increasing the substrate temperature from 270 K to 620 *** found that the growth mode depends strongly on ES barrier over the whole temperatures and the deposition rate ofatoms effectively affects the growth *** simulation results are consistent with many experimental observationsfor homoexpitaxy on a Pt(111)substrate.

关键词： growth mode transition Monte Carlo simulation surface roughness oscillation

Irregular wavelet frames on L^2 (R^n)

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science china mathematics 2005年第2期48卷 277-287页

作者： YANG Deyun & ZHOU Xingwei Department of information & Technology, Nankai university, Tianjin 300071, china Department of mathematics, Nankai university, Tianjin 300071, china Department of Computer science, Taishan college, Taian 271000, china Department of information & Technology Nankai University Tianjin China Department of mathematics Nankai University Tianjin China Department of Computer science Taishan College Taian China

In this paper, we present the conditions on dilation parameter {sj}j that ensure a discrete irregular wavelet system to be a frame on L2(Rn), and for the wavelet frame we consider the perturbations of translation para... 详细信息

关键词： wavelet transform, frame, wavelet frame, irregular dilation.

Bloch constant of holomorphic mappings on the unit polydisk of C^n

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science china mathematics 2008年第4期51卷 652-659页

作者： WANG JianFei~(1+) LIU TaiShun~2 1 college of mathematics and Physics information Engineering Zhejiang normal university Jinhua 321004,china 2 Department of mathematics Huzhou Teachers college Huzhou 313000 china college of mathematics and Physics Information Engineering Zhejiang Normal University Jinhua China Department of mathematics Huzhou Teachers College Huzhou China

In this paper,we give a definition of Bloch mappings defined in the unit polydisk D^n, which generalizes the concept of Bloch functions defined in the unit disk *** is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex *** shall establish the corresponding distortion theorems for subfamiliesβ(K)andβ_(loc)(K) of Bloch mappings defined in the polydisk D^n,which extend the distortion theorems of Liu and Minda to higher *** an application,we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloeh mappings defined in D^*** particular,our results reduce to the classical results of Ahlfors and Landau when n=1.

关键词： Bloch constant Bloch mapping univalent ball critical point Julia lemma locally biholomorphic mapping Landau constant

Finite automata based on quantum logic and monadic second-order quantum logic

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science china(information sciences) 2010年第1期53卷 101-114页

作者： LI YongMing college of Computer science, Shaanxi normal university, Xi’an 710062, china college of Computer science Shaanxi Normal University Xi’an China

We introduce monadic second-order quantum logic and prove that the behaviors of finite automata based on quantum logic are precisely the quantum languages definable with sentences of our monadic secondorder quantum logic. This generalizes Büchi’s and Elgot’s fundamental theorems to quantum logic setting. We also consider first-order quantum logic and show that star-free quantum languages and aperiodic quantum languages introduced here coincide with the first-order quantum definable ones. This generalizes Schützenberger’s fundamental theorems to quantum logic setting. The determinazation of finite automata based on quantum logic is studied by introducing the generalized subset construction method. Then the Kleene theorem in the frame of quantum logic is presented here.

关键词： quantum logic finite automaton monadic second quantum logic quantum language quantum computation Kleene theorem

On solving equations of algebraic sum of equal powers

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science china mathematics 2006年第9期49卷 1153-1157页

作者： WANG Xinghua & YANG Shijun Department of mathematics, Zhejiang university, Hangzhou 310028, china Department of mathematics, Hangzhou normal college, Hangzhou 310036, china Department of mathematics Zhejiang University Hangzhou China Department of mathematics Hangzhou Normal College Hangzhou China

It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.

关键词： algebraic sum of equal powers, Newton's identities, system of equations,roots of a polynomial.