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On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices

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Journal of Systems Science & Complexity 2024年第3期37卷 1295-1307页

作者： lu dong WANG Dingkang XIAO Fanghui School of Mathematics Southwest Jiaotong UniversityChengdu 610031China KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is *** key idea is to establish a relationship between a matrix and any of its full row rank *** on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system *** examples are given to illustrate the effectiveness of the algorithm,and experimental data shows that the algorithm is efficient.

关键词： Free modules Grobner bases minor left prime(MLP) multivariate polynomial matrices polynomial matrix factorizations

Event-triggered receding horizon control via actor-critic design

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Science China(Information Sciences) 2020年第5期63卷 131-145页

作者： lu dong Xin YUAN Changyin SUN School of Automation Southeast University College of Electronics and Information Engineering Tongji University Key Laboratory of Measurement and Control of Complex Systems of Engineering Ministry of EducationSoutheast University

In this paper, we propose a novel event-triggered near-optimal control for nonlinear continuoustime systems. The receding horizon principle is utilized to improve the system robustness and obtain better dynamic control performance. In the proposed structure, we first decompose the infinite horizon optimal control into a series of finite horizon optimal problems. Then a learning strategy is adopted, in which an actor network is employed to approximate the cost function and an critic network is used to learn the optimal control law in each finite horizon. Furthermore, in order to reduce the computational cost and transmission cost, an event-triggered strategy is applied. We design an adaptive trigger condition, so that the signal transmissions and controller updates are conducted in an aperiodic way. Detailed stability analysis shows that the nonlinear system with the developed event-triggered optimal control policy is asymptotically *** results on a single-link robot arm with different noise types have demonstrated the effectiveness of the proposed method.

关键词： event-triggered control receding horizon control actor-critic design optimal control nonlinear systems neural networks

Hybrid Q-learning for data-based optimal control of non-linear switching system

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Journal of Systems Engineering and Electronics 2022年第5期33卷 1186-1194页

作者： LI Xiaofeng dong lu SUN Changyin School of Automation Southeast UniversityNanjing 210096China School of Artificial Intelligence Anhui UniversityHefei 230601China School of Cyber Science and Engineering Southeast UniversityNanjing 211189China

In this paper,the optimal control of non-linear switching system is investigated without knowing the system ***,the Hamilton-Jacobi-Bellman(HJB)equation is derived with the consideration of hybrid action ***,a novel data-based hybrid Q-learning(HQL)algorithm is proposed to find the optimal solution in an iterative *** addition,the theoretical analysis is provided to illustrate the convergence and optimality of the proposed ***,the algorithm is implemented with the actor-critic(AC)structure,and two linear-in-parameter neural networks are utilized to approximate the *** results validate the effectiveness of the data-driven method.

关键词： switching system hybrid action space optimal control reinforcement learning hybrid Q-learning(HQL)

Data-Based Optimal Tracking of Autonomous Nonlinear Switching Systems

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IEEE/CAA Journal of Automatica Sinica 2021年第1期8卷 227-238页

作者： Xiaofeng Li lu dong Changyin Sun the School of Automation Southeast UniversityNanjing 210096 the Key Laboratory of Measurement and Control of Complex Systems of Engineering Ministry of EducationSoutheast UniversityNanjing 210096China the College of Electronics and Information Engineering Tongji UniversityShanghai 201804China

In this paper,a data-based scheme is proposed to solve the optimal tracking problem of autonomous nonlinear switching *** system state is forced to track the reference signal by minimizing the performance ***,the problem is transformed to solve the corresponding Bellman optimality equation in terms of the Q-function(also named as action value function).Then,an iterative algorithm based on adaptive dynamic programming(ADP)is developed to find the optimal solution which is totally based on sampled *** linear-in-parameter(LIP)neural network is taken as the value function *** the presence of approximation error at each iteration step,the generated approximated value function sequence is proved to be boundedness around the exact optimal solution under some verifiable ***,the effect that the learning process will be terminated after a finite number of iterations is investigated in this paper.A sufficient condition for asymptotically stability of the tracking error is ***,the effectiveness of the algorithm is demonstrated with three simulation examples.

关键词： Adaptive dynamic programming approximation error data-based control Q-learning switching system

Day-ahead scheduling based on reinforcement learning with hybrid action space

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Journal of Systems Engineering and Electronics 2022年第3期33卷 693-705页

作者： CAO Jingyu dong lu SUN Changyin School of Automation Southeast UniversityNanjing 210096China School of Cyber Science and Engineering Southeast UniversityNanjing 211189China

Driven by the improvement of the smart grid,the active distribution network(ADN)has attracted much attention due to its characteristic of active *** making full use of electricity price signals for optimal scheduling,the total cost of the ADN can be ***,the optimal dayahead scheduling problem is challenging since the future electricity price is ***,in ADN,some schedulable variables are continuous while some schedulable variables are discrete,which increases the difficulty of determining the optimal scheduling *** this paper,the day-ahead scheduling problem of the ADN is formulated as a Markov decision process(MDP)with continuous-discrete hybrid action ***,an algorithm based on multi-agent hybrid reinforcement learning(HRL)is proposed to obtain the optimal scheduling *** proposed algorithm adopts the structure of centralized training and decentralized execution,and different methods are applied to determine the selection policy of continuous scheduling variables and discrete scheduling *** simulation experiment results demonstrate the effectiveness of the algorithm.

关键词： day-ahead scheduling active distribution network(ADN) reinforcement learning hybrid action space

An Improvement of the Rational Representation for High-Dimensional Systems

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Journal of Systems Science & Complexity 2021年第6期34卷 2410-2427页

作者： XIAO Fanghui lu dong MA Xiaodong WANG Dingkang KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang UniversityBeijing 100191China School of Mathematical Sciences Beihang UniversityBeijing 100191China College of Science China Agricultural UniversityBeijing 100083China

Based on the rational univariate representation of zero-dimensional polynomial systems,Tan and Zhang proposed the rational representation theory for solving a high-dimensional polynomial system,which uses so-called rational representation sets to describe all the zeros of a high-dimensional polynomial *** paper is devoted to giving an improvement for the rational *** idea of this improvement comes from a minimal Dickson basis used for computing a comprehensive Grobner system of a parametric polynomial system to reduce the number of *** authors replace the normal Grobner basis G satisfying certain conditions in the original algorithm(Tan-Zhang’s algorithm)with a minimal Dickson basis G_(m) of a Grobner basis for the ideal,where G_(m) is smaller in size than *** on this,the authors give an improved ***,the proposed algorithm has been implemented on the computer algebra system *** data and its performance comparison with the original algorithm show that it generates fewer branches and the improvement is rewarding.

关键词： Comprehensive Grobner systems high-dimensional polynomial system rational representation rational univariate representation

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A Survey on Algorithms for Computing Comprehensive Gröbner Systems and Comprehensive Gröbner Bases

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Journal of Systems Science & Complexity 2019年第1期32卷 234-255页

作者： lu dong SUN Yao WANG Dingkang KLMM Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences SKLOIS Institute of Information EngineeringChinese Academy of Sciences

Weispfenning in 1992 introduced the concepts of comprehensive Gr?bner system/basis of a parametric polynomial system, and he also presented an algorithm to compute them. Since then,this research ?eld has attracted much attention over the past several decades, and many effcient algorithms have been proposed. Moreover, these algorithms have been applied to many different ?elds,such as parametric polynomial equations solving, geometric theorem proving and discovering, quanti?er elimination, and so on. This survey brings together the works published between 1992 and 2018, and we hope that this survey is valuable for this research area.

关键词： Comprehensive Gröbner basis comprehensive Gröbner system discovering geometric theorems mechanically parametric polynomial system quantifier elimination

Prototype for logging system calls and its overhead analysis

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Journal of Systems Engineering and Electronics 2007年第3期18卷 661-666,F0003页

作者： Meng Jiangtao lu Xianliang dong Guishan School of Computer Science and Engineering Univ. of Electronic Science and Technology of China Chendu 610054 P. R. China

With the capability of the virtual machine monitor, a novel approach for logging system activities is designed. In the design, the guest operating system runs on the virtual machine monitor as non-privileged mode. The redirecting and monitoring modules are added into the virtual machine monitor. When a guest application is calling a system call, it is trapped and redirected from the least privileged level into the virtual machine monitor running in the most privileged level. After logging is finished. it returns to the guest operating system running in the more privileged level and starts the system call. Compared with the traditional methods for logging system activities, the novel method makes it more difficult to destroy or tamper the logs. The preliminary evaluation shows that the prototype is simple and efficient.

关键词： virtual machine monitor virtual monitor Xen guest operating system hyper call system call.

A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

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Journal of Systems Science & Complexity 2018年第6期31卷 1633-1646页

作者： lu dong SUN Yao WANG Dingkang KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China SKLOIS Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China.

This paper presents a new algorithm for computing the extended Hensel construction(EHC) of multivariate polynomials in main variable x and sub-variables u1, u2, ···, um over a number field K. This algorithm first constructs a set by using the resultant of two initial coprime factors w.r.t. x, and then obtains the Hensel factors by comparing the coefficients of xi on both sides of an equation. Since the Hensel factors are polynomials of the main variable with coefficients in fraction field K(u1, u2, ···, um), the computation cost of handling rational functions can be high. Therefore,the authors use a method which multiplies resultant and removes the denominators of the rational functions. Unlike previously-developed algorithms that use interpolation functions or Grobner basis, the algorithm relies little on polynomial division, and avoids multiplying by different factors when removing the denominators of Hensel factors. All algorithms are implemented using Magma, a computational algebra system and experiments indicate that our algorithm is more efficient.

关键词： Extended Hensel construction multivariate polynomial resultant sylvester matrix