An Enhanced Full-Form Model-Free Adaptive Controller for SISO Discrete-Time Nonlinear Systems

This study focuses on the full-form model-free adaptive controller (FFMFAC) for SISO discrete-time nonlinear systems, and proposes enhanced FFMFAC. The proposed technique design incorporates long short-term memory neural networks (LSTMs) and fuzzy neural networks (FNNs). To be more precise, LSTMs are utilized to adjust vital parameters of the FFMFAC online. Additionally, due to the high nonlinear approximation capabilities of FNNs, pseudo gradient (PG) values of the controller are estimated online. EFFMFAC is characterized by utilizing the measured I/O data for the online training of all introduced neural networks and does not involve offline training and specific models of the controlled system. Finally, the rationality and superiority are verified by two simulations and a supporting ablation analysis. Five individual performance indices are given, and the experimental findings show that EFFMFAC outperforms all other methods. Especially compared with the FFMFAC, EFFMFAC reduces the RMSE by 21.69% and 11.21%, respectively, proving it to be applicable for SISO discrete-time nonlinear systems.     

A Communication Multiplexer Problem: Two Alternating Queues with Dependent Randomly-Timed Gated Regime

Two random traffic streams are competing for the service time of a single server (multiplexer). The streams form two queues, primary (queue 1) and secondary (queue 0). The primary queue is served exhaustively, after which the server switches over to queue 0. The duration of time the server resides in the secondary queue is determined by the dynamic evolution in queue 1. If there is an arrival to queue 1 while the server is still working in queue 0, the latter is immediately gated, and the server completes service there only to the gated jobs, upon which it switches back to the primary queue. We formulate this system as a two-queue polling model with a single alternating server and with randomly-timed gated (RTG) service discipline in queue 0, where the timer there depends on the arrival stream to the primary queue. We derive Laplace–Stieltjes transforms and generating functions for various key variables and calculate numerous performance measures such as mean queue sizes at polling instants and at an arbitrary moment, mean busy period duration and mean cycle time length, expected number of messages transmitted during a busy period and mean waiting times. Finally, we present graphs of numerical results comparing the mean waiting times in the two queues as functions of the relative loads, showing the effect of the RTG regime.     

A finite‐capacity queue with exhaustive vacation/close‐down/setup times and Markovian arrival processes

We consider a finitecapacity singleserver vacation model with closedown/setup times and Markovian arrival processes (MAP). The queueing model has potential applications in classical IP over ATM or IP switching systems, where the closedown time corresponds to an inactive timer and the setup time to the time delay to set up a switched virtual connection (SVC) by the signaling protocol. The vacation time may be considered as the time period required to release an SVC or as the time during which the server goes to set up other SVCs. By using the supplementary variable technique, we obtain the queue length distribution at an arbitrary instant, the loss probability, the setup rate, as well as the Laplace–Stieltjes transforms of both the virtual and actual waiting time distributions.     

Non-stationary waiting times in a closed exponential tandem queue

A closed exponential tandem queue in which every customer has to be served by two servers is considered. Given the numbers of customers lined up at each of the two servers, we derive the probability distributions of the waiting time of any customer until his second service is completed, and of the total busy time of the system.     

On the discrete-time regulator problem in infinite-dimensional spaces

The linear, discrete-time regulator problem is considered in infinite-dimensional spaces without posing in advance any positivity conditions on quadratic criterion. The convergence of the finite-time optimum solution is studied, when time increases to infinity with a stable, stabilizable, and detectable system.The author thanks Professors P. Karttunen and H. Koivo for helpful discussions regarding this note.     

Analysis of Queueing Systems with Synchronous Single Vacation for Some Servers

We study a multi-server M/M/c type queue with a single vacation policy for some idle servers. In this queueing system, if at a service completion instant, any d (d c) servers become idle, these d servers will take one and only one vacation together. During the vacation of d servers, the other c–d servers do not take vacation even if they are idle. Using a quasi-birth-and-death process and the matrix analytic method, we obtain the stationary distribution of the system. Conditional stochastic decomposition properties have been established for the waiting time and the queue length given that all servers are busy.     

An optimal service rate in a Poisson arrival queue with two-stage service policy*

We consider a two-stage service policy for a Poisson arrival queueing system. The idle server starts to work with ordinary service rate when a customer arrives. If the number of customers in the system reaches N, the service rate gets faster and continues until the system becomes empty. Otherwise, the server finishes the busy period with ordinary service rate. After assigning various operating costs to the system, we show that there exists a unique fast service rate minimizing the long-run average cost per unit time.This work was supported by Korea Research Foundation Grant(KRF-2002-070-C00021).     

Asymptotic Behavior of Loss Probability in GI/M/1/K Queue as K Tends to Infinity

We obtain an asymptotic behavior of the loss probability for the GI/M/1/K queue as K for cases of <1, >1 and =1.     

Optimal monotone hysteretic Markov policies in anM/M/1 queueing model with switching costs and finite time horizon

In anM/M/1 queueing model, a decision maker can choosem pairs of arrival- and service rates. He can change his action at any time epoch, a switch of action costs an amount depending on the size of the switch. Besides that there are continuously incurring costs. Over a finite time horizon, there exists an optimal monotone hysteretic Markov policy. This is shown essentially by the technique of time discretization.The work producing this article was done during a half year stay at the University of Leiden, The Netherlands, with Prof. Arie Hordijk. A technical report (a more detailled version of this article) was written there [6]. The opportunity for this stay was given by the University of Bonn, Germany, where the author, at that time, worked as scientific assistant of Prof. M. Schäl.     

电压反馈型DC-DC变换器的稳定性研究

建立了电压反馈型DC-DC变换器连续运行模式下的频闪映射模型，利用离散映射方程的Jacobian矩阵的特征值分析了变换器在参数变化时不动点的失稳情况. 以具体的电压反馈型buck变换器为例， 通过理论分析与数值仿真，两者的结果具有很好的一致性，表明利用离散映射分析DC-DC变换器的稳定性是切实可行的. 关键词： 离散映射模型 DC-DC变换器 稳定性