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Optimal Fixed-Point Tracking Control for Discrete-Time Nonlinear Systems via ADP

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IEEE/CAA Journal of Automatica Sinica 2019年第3期6卷 657-666页

作者： Ruizhuo Song liao Zhu IEEE the School of Automation and Electrical Engineering University of Science and Technology Beijing

Based on adaptive dynamic programming(ADP),the fixed-point tracking control problem is solved by a value iteration(VI) algorithm. First, a class of discrete-time(DT)nonlinear system with disturbance is considered. Second, the convergence of a VI algorithm is given. It is proven that the iterative cost function precisely converges to the optimal value,and the control input and disturbance input also converges to the optimal values. Third, a novel analysis pertaining to the range of the discount factor is presented, where the cost function serves as a Lyapunov function. Finally, neural networks(NNs) are employed to approximate the cost function, the control law, and the disturbance law. Simulation examples are given to illustrate the effective performance of the proposed method.

关键词： Adaptive dynamic programming (ADP) fixedpoint tracking optimal control

Analytic approximations of Von Krmn plate under arbitrary uniform pressure—equations in integral form

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Science China(Physics,Mechanics & Astronomy) 2018年第1期61卷 57-67页

作者： XiaoXu Zhong ShiJun liao School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Collaborative Innovative Center for Advanced Ship and Deep-Sea Exploration State Key Laboratory of Ocean Engineering Ministry-of-Education Key Laboratory of Scientific and Engineering Computing

Analytic approximations of the Von Karman＇s plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method （HAM）, an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c1 and c2 in the frame of the HAM. Besides, it is found that the HAM- based iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c1= -0 and c2 = -1, where 0 denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c1 = -0 and c2= -1. In addition, we prove that the HAM approach for the Von karman＇s plate equations in differential form is just a special case of the HAM for the Von karman＇s plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems, and its superiority over perturbation techniques.

关键词： circular plate high nonlinearity homotopy analysis method

ON THE COMPLEXITY OF THE NORMAL BASES VIA PRIME GAUSS PERIOD OVER FINITE FIELDS

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Journal of Systems Science & Complexity 2009年第3期22卷 395-406页

作者： Qunying liao Keqin FENG College of Mathematics and Software Science Sichuan Normal University Chengdu 610066 China Departmentof Mathematical Sciences Tsinghua University Beijing 100084 China. Department of Mathematical Sciences Tsinghua University Beijing 100084 China.

A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic ***,the authors determine explicitly thecomplexity of such normal bases and their dual bases in several cases where the related cyclotomicnumbers have been ***,the authors find several series of such normal bases withlow complexity.

关键词： Complexity cyclotomic number finite field Gauss period normal basis.

Clean numerical simulation:a new strategy to obtain reliable solutions of chaotic dynamic systems

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Applied Mathematics and Mechanics(English Edition) 2018年第11期39卷 1529-1546页

作者： Xiaoming LI Shijun liao School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China State Key Laboratory of Ocean Engineering Shanghai 200240China Collaborative Innovative Center for Advanced Ship and Deep-Sea Exploration Shanghai 200240China Ministry-of-Education Key Laboratory of Scientific and Engineering Computing Shanghai 200240China

It is well-known that chaotic dynamic systems, e.g., three-body system and turbulent flow, have sensitive dependence on the initial conditions(SDIC). Unfortunately,numerical noises, i.e., truncation error and round-off error, always exist in practice. Thus,due to the SDIC, the long-term accurate prediction of chaotic dynamic systems is practically impossible. In this paper, a new strategy for chaotic dynamic systems, i.e., the clean numerical simulation(CNS), is briefly described, and applied to a few Hamiltonian chaotic systems. With negligible numerical noises, the CNS can provide convergent(reliable) chaotic trajectories in a long enough interval of time. This is very important for Hamiltonian systems, and thus should have many applications in various fields. It is found that the traditional numerical methods in double precision cannot give not only reliable trajectories but also reliable Fourier power spectra and autocorrelation functions(ACFs). In addition, even the statistic properties of chaotic systems cannot be correctly obtained by means of traditional numerical algorithms in double precision, as long as these statistics are time-dependent. The CNS results strongly suggest that one had better be very careful on the direct numerical simulation(DNS) results of statistically unsteady turbulent flows, although DNS results often agree well with experimental data when the turbulent flow is in a statistical stationary state.

关键词： chaos numerical noise clean numerical simulation(CNS) reliability of computation

On the Intersection of Binary Linear Codes

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Journal of Systems Science & Complexity 2016年第3期29卷 814-824页

作者： liao Dajian LIU Zihui College of Science Huaihai Institute of Technology Department of Mathematics Beijing Institute of Technology

For a binary linear code,a new relation between the intersection and(2,2)-separating property is addressed,and a relation between the intersection and the trellis complexity is also *** above relations,the authors will apply several classes of binary codes to secret sharing scheme and determine their trellis complexity and separating *** authors also present the properties of the intersection of certain kinds of two-weight binary *** using the concept of value function,the intersecting properties of general binary codes are described.

关键词： Minimal access structure minimal codeword separating property trellis complexity two- weight code value function.

Improved Oustaloup approximation of fractional-order operators using adaptive chaotic particle swarm optimization

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Journal of Systems Engineering and Electronics 2012年第1期23卷 145-153页

作者： Zhe Gao Xiaozhong liao School of Automation Beijing Institute of Technology Beijing 100081 P. R. China

A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization （PSO）. The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.

关键词： fractional-order calculus rational approximation particle swarm optimization (PSO) tent map.

CALCULATION MODEL OF SURFACE TENSION FOR ALLOY MELTS

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中国有色金属学会会刊：英文版 1998年第3期8卷 155-160页

作者： Cheng, Guoguang liao, Nengbin Univ of Science and Technology Beijing Beijing China

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关键词： alloy melt surface tension activity mass action concentration

An explicit method for numerical simulation of wave equations

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Earthquake Engineering and Engineering Vibration 2009年第1期8卷 17-28页

作者： Liu Heng liao Zhenpeng Institute of Engineering Mechanics China Earthquake Administration Harbin 150080 China Department of Shipbuilding and Ocean Engineering University of Engineering Harbin 150001 China

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.

关键词： wave equation numerical simulation explicit recursion formula finite element method

Corrosion Behavior of Extruded near Eutectic Al—Si—Mg and 6063 Alloys

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Journal of Materials Science & Technology 2013年第4期29卷 380-386页

作者： Yuna Wu Hengcheng liao School of Materials Science and Engineering Southeast UniversityJiangsu Key Laboratory for Advanced Metallic MaterialsCampus of Southeast University

In this work, a comparison study on corrosion behavior of extruded near eutectic Al-12.3%Si-0.26%Mg and 6063 alloys has been carried out by mass loss test in 4% H2SO4 aqueous solution in the open air and potentiodynamic polarization test in 3.5 wt.% NaCI aqueous solution. Results indicate that the corrosion resistance of the near eutectic AI-Si-Mg alloy is less than that of 6063 alloy. Macro/microscopy and scanning electron microscopy results clearly show the difference of the corrosion progress of these two alloys in 4% H2SO4 aqueous solution. The corrosion type of 6063 alloy is pitting corrosion. The Mg2Si and AIFeSi particles and surface defects act as nucleation sites for pitting, and the amount and distribution of them have a significant effect on the pitting behavior. For the near eutectic alloy, there are two types of corrosion cells. One is between the extruded primary α-AI and the eutectic, the other is between the eutectic AI and eutectic Si particles. Combination of these two types of corrosion cells leads to a lower corrosion resistance, a higher mass loss of the near eutectic alloy compared with 6063 alloy, and the formation of the paralleling corroded grooves.

关键词： AI-Si alloy 6063 Alloy Corrosion mechanism Pitting Microstructure Potentiodynamic polarization