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An asymptotically optimal nonparametric adaptive controller

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Science China(Technological Sciences) 2000年第6期43卷 561-568页

作者：郭雷谢亮亮 Institute of Systems Science Chinese Academy of Sciences Beijing 100080 China

For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.

关键词： adaptive control nonparametric identification stochastic systems discrete-time optimality.

维普期刊数据库

Chaotic invariant sets of a delayed discrete neural network of two non-identical neurons

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Science China Mathematics 2013年第9期56卷 1869-1878页

作者： CHEN YuanLong HUANG Yu ZOU XingFu Department of Applied Mathematics Guangdong University of Finance Department of Mathematics Sun Yat-sen University Department of Applied Mathematics the University of Western Ontario

In this paper, we show that a delayed discrete Hopfield neural network of two nonidentical neurons with no self-connections can demonstrate chaotic behavior in a region away from the origin. To this end, we first transform the model, by a novel way, into an equivalent system which enjoys some nice properties. Then, we identify a chaotic invariant set for this system and show that the system within this set is topologically conjugate to the full shift map on two symbols. This confirms chaos in the sense of Devaney. Our main result is complementary to the results in Kaslik and Balint (2008) and Huang and Zou (2005), where it was shown that chaos may occur in neighborhoods of the origin for the same system. We also present some numeric simulations to demonstrate our theoretical results.

关键词： neural network Devaney chaos discrete-time topological conjugacy

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On Finite time Ruin Probability with Random Interest Rate in a Multi-Risk Model

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Journal of Mathematical Research with Applications 2014年第4期34卷 492-504页

作者： Jinghai FENG Lixin SONG Linna YI School of Mathematical Sciences Dalian University of TechnologyLiaoning 116024P. R. China

In this paper, assuming that there are s types of insurance contracts in an insurance company, we study the asymptotic of the finite-time ruin probability for the discrete-time multi-risk model.

关键词： ruin probability discrete-time multi-risk model

Bifurcation Analysis of Reduced Network Model of Coupled Gaussian Maps for Associative Memory

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International Journal of Modern Nonlinear Theory and Application 2019年第1期8卷 1-16页

作者： Mio Kobayashi Tetsuya Yoshinaga Department of Creative Technology Engineering National Institute of Technology Anan College Anan Japan Graduate School of Biomedical Sciences Tokushima University Tokushima Japan

This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can generate various phenomena including asymmetric fixed and periodic points. The Gaussian associative memory can effectively recall one of the stored patterns, which were triggered by an input pattern by associating the asymmetric two-periodic points observed in the coupled system with the binary values of output patterns. To investigate the Gaussian associative memory model, we formed its reduced model and analyzed the bifurcation structure. Pseudo-patterns were observed for the proposed model along with other conventional associative memory models, and the obtained patterns were related to the high-order or quasi-periodic points and the chaotic trajectories. In this paper, the structure of the Gaussian associative memory and its reduced models are introduced as well as the results of the bifurcation analysis are presented. Furthermore, the output sequences obtained from simulation of the recalling process are presented. We discuss the mechanism and the characteristics of the Gaussian associative memory based on the results of the analysis and the simulations conducted.

关键词： Gaussian Map Associative Memory Model Bifurcation Analysis discrete-time Dynamical System

Performance Analysis of Two Priority Queuing Systems in Tandem

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American Journal of Operations Research 2012年第4期2卷 509-518页

作者： Faouzi Kamoun College of Technological Innovation Zayed University Dubai UAE

In this paper, we consider a tandem of two head-of-line (HOL) non-preemptive priority queuing systems, each with a single server and a deterministic service-time. Two classes of traffic are considered, namely high priority and low priority traffic. By means of a generating function approach, we present a technique to derive closed-form expressions for the mean buffer occupancy at each node and mean delay. Finally, we illustrate our solution technique with some numerical examples, whereby we illustrate the starvation impact of the HOL priority scheduling discipline on the performance of the low-priority traffic stream. Our research highlights the important fact that the unfairness of the HOL priority scheduling becomes even more noticeable at the network level. Thus this priority mechanism should be used with caution.

关键词： Priority Queuing System Tandem Queues Performance Analysis discrete-time Queues

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

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Applied Mathematics 2018年第2期9卷 153-170页

作者： A. Lorente M. S. Sánchez Departamento de Matemáticas y Computación Universidad de Burgos Escuela Politécnica Superior Avda. Cantabria s/n 09006 Burgos Spain Departamento de Matemáticas y Computación Universidad de Burgos Facultad de Ciencias Pza. Misael Ba&ntilde uelos s/n 09001 Burgos Spain

This paper analyzes a discrete-time Geoa/Geob/1 queuing system with batch arrivals of fixed size a, and batch services of fixed size b. Both arrivals and services occur randomly following a geometric distribution. The steady-state queue length distribution is obtained as the solution of a system of difference equations. Necessary and sufficient conditions are given for the system to be stationary. Besides, the uniqueness of the root of the characteristic polynomial in the interval (0, 1) is proven which is the only root needed for the computation of the theoretical solution with the proposed procedure. The theoretical results are compared with the ones observed in some simulations of the queuing system under different sets of parameters. The agreement of the results encourages the use of simulation for more complex systems. Finally, we explore the effect of parameters on the mean length of the queue as well as on the mean waiting time.

关键词： discrete-time Queuing System Batch Arrivals Batch Services Stationary Systems

Stationary Analysis of Geo/Geo/1 Queue with Two-Speed Service and the Optimal Switching Threshold for the Service Rate

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Applied Mathematics 2015年第6期6卷 908-921页

作者： Xudong Lin School of Science Sichuan University of Science and Engineering Zigong China

This paper considers a Geo/Geo/1 queueing system with infinite capacity, in which the service rate changes depending on the workload. Initially, when the number of customers in the system is less than a certain threshold L, low service rate is provided for cost saving. On the other hand, the high service rate is activated as soon as L customers accumulate in the system and such service rate is preserved until the system becomes completely empty even if the number of customers falls below L. The steady-state probability distribution and the expected number of customers in the system are derived. Through the first-step argument, a recursive algorithm for computing the first moment of the conditional sojourn time is obtained. Furthermore, employing the results of regeneration cycle analysis, the direct search method is also implemented to determine the optimal value of L for minimizing the long-run average cost rate function.

关键词： Workload-Dependent Service Switching Threshold discrete-time Queue Sojourn time Regeneration Cycle

Advancements in time Modeling: Relationalism, Divisional Structures, and Geometry

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Journal of Applied Mathematics and Physics 2024年第10期12卷 3358-3383页

作者： Steven D. P. Moore Independent Researcher Milton Canada

This article broadens terminology and approaches that continue to advance time modelling within a relationalist framework. time is modeled as a single dimension, flowing continuously through independent privileged points. Introduced as absolute point-time, abstract continuous time is a backdrop for concrete relational-based time that is finite and discrete, bound to the limits of a real-world system. We discuss how discrete signals at a point are used to temporally anchor zero-temporal points [t = 0] in linear time. Object-oriented temporal line elements, flanked by temporal point elements, have a proportional geometric identity quantifiable by a standard unit system and can be mapped on a natural number line. Durations, line elements, are divisible into ordered unit ratio elements using ancient timekeeping formulas. The divisional structure provides temporal classes for rotational (Rt24t) and orbital (Rt18) sample periods, as well as a more general temporal class (Rt12) applicable to either sample or frame periods. We introduce notation for additive cyclic counts of sample periods, including divisional units, for calendar-like formatting. For system modeling, unit structures with dihedral symmetry, group order, and numerical order are shown to be applicable to Euclidean modelling. We introduce new functions for bijective and non-bijective mapping, modular arithmetic for cyclic-based time counts, and a novel formula relating to a subgroup of Pythagorean triples, preserving dihedral n-polygon symmetries. This article presents a new approach to model time in a relationalistic framework.

关键词： Relationalism Mohist Geometry Euclidean Geometry Relational-time discrete-time Continuous-time Planck time Zero-time

Expansion of the Decoupled Discreet-time Jacobian Eigenvalue Approximation for Model-Free Analysis of PMU Data

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Journal of Power and Energy Engineering 2017年第6期5卷 14-35页

作者： Sean D. Kantra Elham B. Makram Holcombe Department of Electrical and Computer Engineering Clemson University Clemson USA

This paper proposes an extension of the algorithm in [1], as well as utilization of the wavelet transform in event detection, including High Impedance Fault (HIF). Techniques to analyze the abundant data of PMUs quickly and effectively are paramount to increasing response time to events and unstable parameters. With the amount of data PMUs output, unstable parameters, tie line oscillations, and HIFs are often overlooked in the bulk of the data. This paper explores model-free techniques to attain stability information and determine events in real-time. When full system connectivity is unknown, many traditional methods requiring other bus measurements can be impossible or computationally extensive to apply. The traditional method of interest is analyzing the power flow Jacobian for singularities and system weak points, attained by applying singular value decomposition. This paper further develops upon the approach in [1] to expand the discrete-time Jacobian Eigenvalue Approximation (DDJEA), giving values to significant off-diagonal terms while establishing a generalized connectivity between correlated buses. Statistical linear models are applied over large data sets to prove significance to each term. Then the off diagonal terms are given time-varying weights to account for changes in topology or sensitivity to events using a reduced system model. The results of this novel method are compared to the present errors of the previous publication in order to quantify the degree of improvement that this novel method imposes. The effective bus eigenvalues are briefly compared to Prony analysis to check similarities. An additional application for biorthogonal wavelets is also introduced to detect event types, including the HIF, for PMU data.

关键词： Synchrophasor PMU openPDC Power Flow Jacobian Decoupled discrete-time Jacobian Approximation (DDJEA) Singular Value Decomposition (SVD) High Impedance Fault (HIF) discrete Wavelet Transform (DWT)