Due-date assignment for multi-server multi-stage assembly systems

In this paper, we attempt to present a constant due-date assignment policy in a multi-server multi-stage assembly system. This system is modelled as a queuing network, where new product orders are entered into the system according to a Poisson process. It is assumed that only one type of product is produced by the production system and multi-servers can be settled in each service station. Each operation of every work is operated at a devoted service station with only one of the servers located at a node of the network based on first come, first served (FCFS) discipline, while the processing times are independent random variables with exponential distributions. It is also assumed that the transport times between each pair of service stations are independent random variables with generalised Erlang distributions. Each product's end result has a penalty cost that is some linear function of its due date and its actual lead time. The due date is calculated by adding a constant to the time that the order enters into the system. Indeed, this constant value is decided at the beginning of the time horizon and is the constant lead time that a product might expect between the time of placing the order and the time of delivery. For computing the due date, we first convert the queuing network into a stochastic network with exponentially distributed arc lengths. Then, by constructing an appropriate finite-state continuous-time Markov model, a system of differential equations is created to find the manufacturing lead-time distribution for any particular product, analytically. Finally, the constant due date for delivery time is obtained by using a linear function of its due date and minimising the expected aggregate cost per product.     

Multi-objective reliability optimization for dissimilar-unit cold-standby systems using a genetic algorithm

A genetic algorithm approach is used to solve a multi-objective discrete reliability optimization problem in a k dissimilar-unit non-repairable cold-standby redundant system. Each unit is composed of a number of independent components with generalized Erlang distributions arranged in a series–parallel configuration. There are multiple component choices with different distribution parameters available for being replaced with each component of the system. The objective of the reliability optimization problem is to select the best components, from the set of available components, to be placed in the standby system in order to minimize the initial purchase cost of the system, maximize the system MTTF (mean time to failure), minimize the system VTTF (variance of time to failure) and also maximize the system reliability at the mission time. Finally, we apply a genetic algorithm with double strings using continuous relaxation based on reference solution updating (GADSCRRSU) to solve this multi-objective problem, using goal attainment formulation. The results are also compared against the results of a discrete-time approximation technique to show the efficiency of the proposed GA approach.     

Predicting departure times in multi-stage queueing systems

We develop an approximation model for the state-dependent sojourn time distribution of customers or orders in a multi-stage, multi-server queueing system, when interarrival and service times can take on general distributions. The model can be used to make probabilistic statements about the departure time of a customer or order, given the number and location of customers currently in process or waiting, and these probabilities can be recomputed while waiting at any point during the sojourn time. The model uses phase-type distributions and a new method to estimate the remaining processing times of customers in service when the sojourn time distribution is computed.     

Quadratic control of stochastic hybrid systems with renewal transitions

We study the quadratic control of a class of stochastic hybrid systems with linear continuous dynamics for which the lengths of time that the system stays in each mode are independent random variables with given probability distribution functions. We derive a condition for finding the optimal feedback policy that minimizes a discounted infinite horizon cost. We show that the optimal cost is the solution to a set of differential equations with unknown boundary conditions. Furthermore, we provide a recursive algorithm for computing the optimal cost and the optimal feedback policy. The applicability of our result is illustrated through a numerical example, motivated by stochastic gene regulation in biology.     

Decentralised output feedback control of Markovian jump interconnected systems with unknown interconnections

The problem of decentralised output feedback control is addressed for Markovian jump interconnected systems with unknown interconnections and general transition rates (TRs) allowed to be unknown or known with uncertainties. A class of decentralised dynamic output feedback controllers are constructed, and a cyclic-small-gain condition is exploited to dispose the unknown interconnections so that the resultant closed-loop system is stochastically stable and satisfies an H_∞ performance. With slack matrices to cope with the nonlinearities incurred by unknown and uncertain TRs in control synthesis, a novel controller design condition is developed in linear matrix inequality formalism. Compared with the existing works, the proposed approach leads to less conservatism. Finally, two examples are used to illustrate the effectiveness of the new results.     

不确定时滞的无线网络控制系统的故障检测

研究了一类具有不确定时滞的无线网络控制系统的故障检测的问题。由于时滞是不确定的,可以通过增广向量法将系统建模为马尔科夫跳变系统。在此基础上,设计了观测滤波器,满足了滤波器在没有扰动的情况下均方指数稳定,在有扰动时,满足一定的H∞鲁棒性能。当系统发生故障时,故障检测系统立即检测出故障。所得结果通过仿真示例得到了验证。     

Probabilistic systems coalgebraically: A survey

We survey the work on both discrete and continuous-space probabilistic systems as coalgebras, starting with how probabilistic systems are modeled as coalgebras and followed by a discussion of their bisimilarity and behavioral equivalence, mentioning results that follow from the coalgebraic treatment of probabilistic systems. It is interesting to note that, for different reasons, for both discrete and continuous probabilistic systems it may be more convenient to work with behavioral equivalence than with bisimilarity.     

Dissipativity‐based asynchronous control of discrete‐time Markov jump systems with mixed time delays

This paper addresses the problem of dissipativity‐based asynchronous control for a class of discrete‐time Markov jump systems. A unified framework to design a controller for discrete‐time Markov jump systems with mixed time delays is proposed, which is fairly general and can be reduced to a synchronous controller or a mode‐independent controller. Based on a stochastic Lyapunov function approach, which fully utilizes available information of the system mode and the controller, a sufficient condition is established to ensure the stochastic stability and strictly ( , , ) dissipative performance of the resulting closed‐loop system. Finally, the effectiveness and validity of the proposed method are illustrated with a simulation example.     

具有双边随机时延和丢包的网络控制系统有限时间控制

针对双边丢包和双边时延的网络化控制系统的有限时间控制问题,通过引入时间偏移量的方法,将丢包转换为时延,从而形成多时延系统,并将时间延迟转换为系统状态延迟。基于全概率公式给出已知网络丢包率下连续丢包的概率公式,用Markov链表征网络时延的变化规律。以线性矩阵不等式的形式给出改进的有限时间时延相关稳定性判据,并通过数值仿真验证所提方法的有效性。     

Genetic algorithm for supply planning in two-level assembly systems with random lead times

This paper examines supply planning for two-level assembly systems under lead time uncertainties. It is supposed that the demand for the finished product and its due date are known. The assembly process at each level begins when all necessary components are in inventory. If the demand for the finished product is not delivered at the due date, a tardiness cost is incurred. In the same manner, a holding cost at each level appears if some components needed to assemble the same semi-finished product arrive before beginning the assembly at this level. It is assumed also that the lead time at each level is a random discrete variable. The expected cost is composed of the tardiness cost for finished product and the holding costs of components at levels 1 and 2. The objective is to find the release dates for the components at level 2 in order to minimize the total expected cost. For this new problem, a genetic algorithm is suggested. The proposed algorithm is evaluated with a variety of supply chain settings in order to verify its robustness across different supply chain scenarios. Moreover, the effect of a local search on the performance of the Genetic Algorithm in terms of solution quality, convergence and computation time is also investigated.     

Iterative learning control for uncertain systems: Noncausal finite time interval robust control design

In this paper, we present a novel robust Iterative Learning Control (ILC) control strategy that is robust against model uncertainty as given by an additive uncertainty model. The design methodology hinges on ??_∞ optimization, but formulated such that the obtained ILC controller is not restricted to be causal, and inherently operates on a finite time interval. Optimization of the robust ILC (R‐ILC) solution is accomplished for the situation where any information about structure in the uncertainty is discarded, and for the situation where the information about the structure in the uncertainty is explicitly taken into account. Subsequently, the convergence and performance properties of resulting R‐ILC controlled system are analyzed. On an experimental set‐up, we show that the presented R‐ILC control strategy can outperform an existing linear‐quadratic norm‐optimal ILC approach and an existing causal R‐ILC approach based on frequency domain ??_∞ synthesis. Copyright © 2010 John Wiley & Sons, Ltd.     

Markov modeling and analysis of multi-stage manufacturing systems with remote quality information feedback

Modeling and analysis of multi-stage manufacturing systems (MMSs) for product quality propagation have attracted a great deal of attention recently. Due to cost and resources constraints, MMSs do not always have ubiquitous inspection, and MMSs with remote quality information feedback (RQIF, i.e., quality inspection operation is conducted at the end of the production line) are widely applied. This paper develops a Markov model to analyze quality propagation in MMSs with RQIF. Analytical expressions of the final product quality are derived and the monotonicity properties are investigated. A quality bottleneck identification method is explored based on the proposed Markov model. The results of case study demonstrate the effectiveness of the proposed model.     

不确定跳变系统反馈预测控制

针对一类受限不确定离散Markov跳变系统,提出一种反馈预测控制器设计方法.为便于工程应用,该方法考虑了各模态下的动态系统参数存在多胞不确定性,以及各模态间的跳变转移概率部分未知的情形.通过优化无穷时域的二次型性能指标来确定预测控制器及其对应的椭圆不变集,控制器保证了闭环系统鲁棒均方稳定.同时,用所求得的控制增益在线构造了一组渐近稳定的多面体不变集,在一定程度上扩大了系统状态可行集的范围.数值示例验证了所提方法的可行性和有效性.     

非线性主动悬架系统自适应最优控制

针对非线性主动悬架系统多性能指标综合优化问题,提出一类自适应最优控制方法.首先,通过引入一阶低通滤波操作,利用系统输入输出构建结构简单且调节参数少的一类未知非线性动态估计器,在线估计系统未知非线性动态;其次,构建包含乘驾舒适度、悬架行程空间及输入能耗的性能指标函数,采用单层神经网络对最优性能指标函数进行在线逼近,并得到新的哈密尔顿函数;为实现在线求解,构建一类新的基于参数估计误差信息的自适应律,在线更新神经网络权值并计算最优控制律;最后,理论分析闭环系统稳定性和收敛性,并通过专业软件Carsim与Matlab/Simulink搭建的联合仿真平台给出的对比仿真结果,验证所提出方法可有效解决主动悬架系统多目标性能优化控制问题,提升主动悬架系统综合性能.     

基于马氏决策过程的概率离散事件系统最优控制

使用马氏决策过程研究了概率离散事件系统的最优控制问题.首先,通过引入费用函数、目标函数以及最优函数的定义,建立了可以确定最优监控器的最优方程.之后,又通过此最优方程获得了给定语言的极大可控、∈-包含闭语言.最后给出了获得最优费用与最优监控器的算法.     

Optimal control of markov chains admitting strong and weak interactions

This paper is devoted to the study of an optimal control problem for a Markov chain with generator B + εA, where ε is a small parameter. It is shown that an approximate solution can be calculated by a policy improvement algorithm involving computations relative to an ‘aggregated’ problem (the dimension of which is given by N, the number of ergodic sets for the B matrix) together with a family of ‘decentralized’ problems (the dimensions of which are given by the number of elements in each ergodic set for the B matrix).     

Solving two-machine assembly scheduling problems with inventory constraints

This paper considers a scheduling problem with component availability constraints in a supply chain consisting of two manufacturing facilities and a merge-in-transit facility. Three mixed-integer programming (MIP) models and a constraint programming (CP) model are compared in an extensive numerical study. Results show that when there are no components shared among the two manufacturers, the MIP model based on time-index variables is the best for proving optimality for problems with short processing times whereas the CP model tends to perform better than the others for problems with a large range of processing times. When shared components are added, the performance of all models deteriorates, with the time-indexed MIP providing the best results. By explicitly modelling the dependence of scheduling decisions on the availability of component parts, we contribute to the literature on the integration of inventory and scheduling decisions, which is necessary for solving realistic supply chain problems.     

Static output feedback control for discrete‐time hidden Markov jump systems against deception attacks

This paper investigates the static output feedback control problem for Markov jump systems subject to asynchronous mode information and deception attacks. A hidden Markov model is employed to observe the unmeasurable system mode. In this case, the asynchronous phenomenon between the controller and the original system is depicted. By using the mode‐dependent Lyapunov function, a sufficient condition is established such that the resulting closed‐loop system is stochastically mean square exponentially ultimately bounded under randomly occurring deception attacks and external disturbance. Based on this condition, the asynchronous static output feedback controller is designed in view of linear matrix inequalities. Finally, the effectiveness and superiority of the presented method are elaborated via a numerical example and a practical example.     

Control of manufacturing systems with a two-value, production-dependent failure rate

In this paper we consider a failure prone, single machine, single part-type, limited inventory, manufacturing system subject to a non-homogeneous Markov failure/repair process with the failure rate depending on the production rate through a two-value function. The problem is to minimize a cost function which includes a penalty for waiting customers. We derive and prove the optimality of a policy which depends on a threshold but is not the so-called hedging point policy, optimal for the Markov homogeneous case.