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A logical network approximation to optimal control on a continuous domain and its application to HEV control

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Science China(Information Sciences) 2022年第11期65卷 178-195页

作者： Yuhu WU Jiangyan ZHANG Tielong SHEN School of Control Science and Engineering Dalian University of Technology College of Mechanical and Electronic Engineering Dalian Minzu University Department of Engineering and Applied Sciences Sophia University

The finite-time horizon optimal control problem is investigated for discrete-time dynamical systems defined on a continuous domain. First, the original optimal control problem in the continuous domain is approximated as one on a finite-valued domain based on a special quantification process. Under suitable assumptions, convergence analysis of the approximate optimal cost of the quantified system to the optimal cost of the original system was established with error estimation. Thereafter, the approximate problem is solved using a logical network-based method that is proposed based on the semi-tensor product of the ***, the proposed scheme is applied to deal with the optimal control problem of a hybrid electric vehicle(HEV) powertrain system, and its effectiveness is shown by a series of simulation results.

关键词： finite horizon optimal control logical networks semi-tensor product quantification HEV control

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Policy Iteration Approach to Average Optimal Control Problems for Boolean Control networks 36

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Policy Iteration Approach to Average Optimal Control Problem...

第36届中国控制会议

作者： Yuhu Wu Ximing Sun Wei Wang Tielong Shen School of Control Science and Engineering Dalian University of Technology Department of Mechanical Engineering Sophia University

ISBN: (纸本)9781538629185

This paper investigates the average infinite horizon optimal control problem for Boolean control networks（BCNs）.Based on the semi-tensor product of matrices and Jordan decomposition technique,an optimality equation for the average infinite horizon problem of BCNs is *** resorting to Laurent series expression,a policy iteration algorithm,which can find the optimal solution in finite iteration steps,is *** applications,the output tracking problem for BCNs and the intervention problem of cAMP receptor protein are investigated.

关键词： Boolean control networks logical networks Semi-tensor product Optimal control Policy iteration

On observability of Galois nonlinear feedback shift registers over finite fields

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Frontiers of Information Technology & Electronic Engineering 2022年第10期23卷 1533-1545页

作者： Zhe GAO Jun’e FENG Yongyuan YU Yanjun CUI School of Mathematics Shandong UniversityJinan 250100China Department of Computer Science&Engineering University of Minnesota Twin CitiesMinneapolisMN 55455USA

Observability ensures that any two distinct initial states can be uniquely determined by their outputs,so the stream ciphers can avoid unobservable nonlinear feedback shift registers(NFSRs)to prevent the occurrence of equivalent *** paper discusses the observability of Galois NFSRs over finite *** NFSRs are treated as logical networks using the semi-tensor *** vector form of the state transition matrix is introduced,by which a necessary and sufficient condition is proposed,as well as an algorithm for determining the observability of general Galois ***,a new observability matrix is defined,which can derive a matrix method with lower computation ***,the observability of two special types of Galois NFSRs,a full-length Galois NFSR and a nonsingular Galois NFSR,is *** methods are proposed to determine the observability of these two special types of NFSRs,and some numerical examples are provided to support these results.

关键词： Observability Nonlinear feedback shift registers(NFSRs) Galois NFSRs Semi-tensor product Finite fields logical networks

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State space optimization of finite state machines from the viewpoint of control theory

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Frontiers of Information Technology & Electronic Engineering 2021年第12期22卷 1598-1609页

作者： Jumei YUE Yongyi YAN Zengqiang CHEN He DENG College of Agricultural Equipment Engineering Henan University of Science and TechnologyLuoyang 471003China College of Information Engineering Henan University of Science and TechnologyLuoyang 471003China College of Artificial Intelligence Nankai UniversityTianjin 300071China

Motivated by the inconvenience or even inability to explain the mathematics of the state space optimization of finite state machines(FSMs)in most existing results,we consider the problem by viewing FSMs as logical dynamic *** ideas from the concept of equilibrium points of dynamic systems in control theory,the concepts of t-equivalent states and t-source equivalent states are *** on the state transition dynamic equations of FSMs proposed in recent years,several mathematical formulations of t-equivalent states and t-source equivalent states are *** can be analogized to the necessary and sufficient conditions of equilibrium points of dynamic systems in control theory and thus give a mathematical explanation of the optimization *** these mathematical formulations,two methods are designed to find all the t-equivalent states and t-source equivalent states of ***,two ways of reducing the state space of FSMs are *** can be implemented without computers but with only pen and paper in a mathematical *** addition,an open question is raised which can further improve these methods into unattended ***,the correctness and effectiveness of the proposed methods are verified by a practical language model.

关键词： Finite state machines Finite-valued systems logical systems logical networks Semi-tensor product of matrices Space optimization

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Finite Input and Given Time Critical Observabilities of Finite State Machines Based on the Semi-tensor Product of Matrices

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Finite Input and Given Time Critical Observabilities of Fini...

第40届中国控制会议

作者： He Deng Yongyi Yan Jumei Yue College of Information Engineering Henan University of Science and Technology College of Agricultural Equipment Engineering Henan University of Science and Technology

The notion of safety in safety-critical applications can be represented by the concept of critical observability. The traditional concept of critical observability refers to possibility of detecting if the current state of a nondeterministic finite state machine（NFSM）belongs to a so-called critical set for any input and any initial state. In practice, the input is always of finite length and we may only care about the state of an FSM at a given time step or the inverse problem that how to find all possible inputs moving the FSM to a critical state of interest. Thus, we propose two new concepts about critical observability, critical observability with finite input and critical observability at a given time step, to cope with these two cases. From the view of algebraic model resulting from the theory of semi-tensor product（STP）, we propose corresponding algebraic criteria and algorithms. They are based on matrix operation, which means that they naturally avoid the design of critical observers and can be solved efficiently by computers.

关键词： logical systems logical networks finite-valued systems finite state machines critical observability semi-tensor product of matrices

logical Approach to Livelock and Deadlock of Deterministic Finite State Machines: Modelling and Finding

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Logical Approach to Livelock and Deadlock of Deterministic F...

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作者： Yongyi Yan Jumei Yue Zengqiang Chen College of Information Engineering Henan University of Science and Technology College of Agricultural Equipment Engineering Henan University of Science and Technology College of Artificial Intelligence Nankai University

Inspired by the connections between logical dynamic systems and continuous variable dynamic systems, this paper addresses the modelling and finding of the livelock and deadlock of deterministic finite state machines（DFSMs） from a logical viewpoint, where a DFSM is viewed as a logical system by treating the input string and current state of a DFSM as the input signal and state of a logical system, respectively. A difference equation-like model is proposed to formulate the dynamics of DFSMs and the behavior of deadlock and livelock of DFSMs. Based on the model and by generalizing livelock and deadlock as a loop structure, a unified discriminate criterion is established by which whether a DFSM contains livelock or dead lock can be judged easily. Further,an algorithm is designed for finding all the livelocks and deadlocks for a given DFSM.

关键词： logical systems logical networks finite-valued systems semi-tensor product of matrices finite state machines logical blocking

Graph Models for Security Monitoring of Streets and Balance Communication of WSNs

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Graph Models for Security Monitoring of Streets and Balance ...

第40届中国控制会议

作者： Yongyi YAN Jumei YUE He DENG College of Information Engineering Henan University of Science and Technology College of Agricultural Equipment Engineering Henan University of Science and Technology

The concepts of k-degree and k-balance control sets of graphs are abstracted from some real-world problems such as the location of cameras for saving resources in street security monitoring and the arrangement of major sensors for balancing load in wireless sensor networks. Then using a new matrix analysis tool, semi-tensor product of matrices（STP） developed in recent years, such two kinds of control sets are formulated by establishing a necessary and sufficient conditions that determine whether or not a vertex subset of a graph is a k-degree control set, and a necessary condition that facilitates finding k-balance control sets of a graph. Finally the effectiveness of the idea and the correctness of the results are verified by studying security monitoring of a street.

关键词： logical systems logical networks finite-valued systems semi-tensor product of matrices