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Safe Q-Learning for Data-Driven Nonlinear Optimal Control With Asymmetric State Constraints

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IEEE/CAA Journal of Automatica Sinica 2024年第12期11卷 2408-2422页

作者： Mingming Zhao ding wang Shijie Song Junfei Qiao the School of Information Science and Technology the Beijing Key Laboratory of Computational Intelligence and Intelligent System the Beijing Laboratory of Smart Environmental Protection and the Beijing Institute of Artificial Intelligence Beijing University of Technology IEEE the School of Mechanical and Electrical Engineering University of Electronic Science and Technology of China

This article develops a novel data-driven safe Q-learning method to design the safe optimal controller which can guarantee constrained states of nonlinear systems always stay in the safe region while providing an optimal performance. First, we design an augmented utility function consisting of an adjustable positive definite control obstacle function and a quadratic form of the next state to ensure the safety and optimality. Second, by exploiting a pre-designed admissible policy for initialization, an off-policy stabilizing value iteration Q-learning(SVIQL) algorithm is presented to seek the safe optimal policy by using offline data within the safe region rather than the mathematical ***, the monotonicity, safety, and optimality of the SVIQL algorithm are theoretically proven. To obtain the initial admissible policy for SVIQL, an offline VIQL algorithm with zero initialization is constructed and a new admissibility criterion is established for immature iterative policies. Moreover, the critic and action networks with precise approximation ability are established to promote the operation of VIQL and SVIQL algorithms. Finally, three simulation experiments are conducted to demonstrate the virtue and superiority of the developed safe Q-learning method.

关键词： Adaptive critic control adaptive dynamic programming (ADP) control barrier functions (CBF) stabilizing value iteration Q-learning (SVIQL) state constraints

Lipschitz estimates for commutator of fractional integral operators on non-homogeneous metric measure spaces

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Applied Mathematics(A Journal of Chinese Universities) 2020年第3期35卷 253-264页

作者： wang ding-huai ZHOU Jiang MA Bo-lin School of Mathematics and Statistics Anhui Normal UniversityWuhu 241000China College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China College of Science and Information Engineering Jiaxing UniversityJiaxing 314001China

In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β) and 1/q = 1/p-(α + β), and obtain their weak(L^1(μ), L^(1/(1-α-β))(μ))-type. Moreover, the authors also consider the boundedness in the case that 1/(α+β) < p < 1/α,1/α≤ p ≤∞ and the endpoint cases, namely, p = 1/(α + β).

关键词： Non-homogeneous space Fractional integral Lipschitz function Commutator Endpoint estimate

Research on the intelligent design system for investment casting die of aero-engine turbine blade based on knowledge

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航空动力学报 2010年第5期25卷 1061-1067页

作者： JIANG Rui-song ZHANG ding-hua wang Wen-hu The Key Laboratory of Contemporary Design and Integrated Manufacturing Ministry of EducationSchool of Mechanical EngineeringNorthwestern Polytechnical UniversityXi'an 710072China

To solve the problems in turbine blade investment casting die design process such as long design time,lacking of expert experience and low level of intelligence,knowledge-based engineering (KBE) was introduced in the turbine blade investment casting die design field. The key technologies of the intelligent design method were researched and a prototype system was developed. A hybrid reasoning model was prompted in which case-based reasoning (CBR) was applied to conceptual design and rule-based reasoning (RBR) was applied to parts design after research the design process and domain knowledge of casting die. In the conceptual design stage,a retrieval model which integrated nearest neighbor approach and knowledge-based retrieval approach was prompted to improve the retrieval efficiency. Meanwhile,RBR was used to modify the retrieval result. The practical application results indicate that this system can reuse the expert experience efficiently and heighten the die design efficiency and quality.

关键词： turbine blade investment casting die intelligent design knowledge-based engineering (KBE)

A magnetic reconnection model for quasi-periodic oscillations in black hole systems

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Research in Astronomy and Astrophysics 2013年第6期13卷 705-718页

作者： Chang-Yin Huang ding-Xiong wang Jiu-Zhou wang Zhi-Yun wang School of Physics Huazhong University of Science and Technology School of Mathematics and Statistics Huazhong University of Science and Technology School of Physics and Electronic Engineering Hubei University of Arts and Science

The quasi-periodic oscillations （QPOs） in black hole （BH） systems with different scales are interpreted based on the magnetic reconnection of large-scale mag- netic fields generated by toroidal electric currents flowing in the inner region of the accretion disk, where the current density is assumed to be proportional to the mass density of the accreting plasma. The magnetic connection （MC） is taken into account in resolving dynamic equations describing the accretion disk, in which the MC be- tween the inner and outer disk regions, between the plunging region and the disk, and between the BH horizon and the disk are involved. It turns out that a single QPO frequency associated with several BH systems with different scales can be fitted by in- voking the magnetic reconnection due to the MC between the inner and outer regions of the disk, including the BH binaries XTE J1859＋226, XTE J1650-500 and GRS 1915＋105 and the massive BHs in NGC 5408 X-1 and RE J1034＋396. In addition, the X-ray spectra corresponding to the QPOs for these sources are fitted based on the typical disk-corona model.

关键词： accretion, accretion disks -- black hole physics -- magnetic fields --stars individual (XTE J1859+226, XTE J1650-500, GRS 1915+105) -- galaxies:individual (NGC 5408, RE J1034+396)

A model of low-frequency quasi-periodic oscillations in black hole X-ray binaries

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Research in Astronomy and Astrophysics 2012年第6期12卷 661-670页

作者： Zhi-Yun wang Chang-Yin Huang ding-Xiong wang Jiu-Zhou wang School of Physics and Electronic Engineering Hubei University of Arts and Science Xiangyang441053 China School of Physics Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China

A model of low-frequency quasi-periodic oscillations （LFQPOs） of black hole X-ray binaries （BHXBs） is proposed based on the perturbed magnetohydrody- namic equations of an accretion disk. It turns out that the LFQPO frequencies of some BHXBs can be fitted by the frequencies of the toroidal Alfv6n wave oscillation cor- responding to the maximal radiation flux. In addition, the positive correlation of the LFQPO frequencies with the radiation flux from an accretion disk is well interpreted.

关键词： accretion accretion disks -- black hole physics -- magnetic fields --stars: individual (XTE J1550-564 GRO J1655--40)

A New Molecular-Dynamics Approach for Fully Relaxed Crystals at Constant Pressure

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Chinese Physics Letters 1997年第10期14卷 764-767页

作者： LIU Gang wang En-ge wang ding-sheng Laboratory for Surface Physics Institute of Physics&Certre for Condensed Matter PhysicsChinese Academy of SciencesBeijing 100080

A new molecular-dynamics method at constant pressure has been *** the three edge vectors of a crystal cell as well as the position vectors of all particles are taken as independent variables,this method allows the crystal to relax ***,the effect of pressure on the crystal structure is explicitly given in this *** an example,the evolution process of cobalt from a structure far from the final one to the ideal hexagonal close packing structure was given.

关键词： crystal structure vectors

Constrained total least squares algorithm for passive location based on bearing-only measurements

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Science in China(Series F) 2007年第4期50卷 576-586页

作者： wang ding ZHANG Li WU Ying Department of Communication Engineering Information Engineering University of PLA Zhengzhou 450002 China

The constrained total least squares algorithm for the passive location is presented based on the bearing-only measurements in this paper. By this algorithm the non-linear measurement equations are firstly transformed into linear equations and the effect of the measurement noise on the linear equation coefficients is analyzed, therefore the problem of the passive location can be considered as the problem of constrained total least squares, then the problem is changed into the optimized question without restraint which can be solved by the Newton algorithm, and finally the analysis of the location accuracy is given. The simulation results prove that the new algorithm is effective and practicable.

关键词： passive location constrained total least squares algorithm Newton algorithm

The structured total least squares algorithm research for passive location based on angle information

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Science in China(Series F) 2009年第6期52卷 1043-1054页

作者： wang ding ZHANG Li WU Ying Institute of Information Engineering PLA Information Engineering University Zhengzhou 450002 China

Based on the constrained total least squares （CTLS） passive location algorithm with bearing-only measurements, in this paper, the same passive location problem is transformed into the structured total least squares （STLS） *** solution of the STLS problem for passive location can be obtained using the inverse iteration *** also expatiates that both the STLS algorithm and the CTLS algorithm have the same location mean squares error under certain ***, the article presents a kind of location and tracking algorithm for moving target by combining STLS location algorithm with Kalman filter （KF）.The efficiency and superiority of the proposed algorithms can be confirmed by computer simulation results.

关键词： passive location angle information least squares total least squares constrained total least squares structured total least squares Kalman filter singular value decomposition QR decomposition

Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space

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Communications in Theoretical Physics 2006年第1X期46卷 97-100页

作者： FANG Jian-Hui ding Ning wang Peng College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The defition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.

关键词： unified symmetry mechanical system conserved quantity phase space