带非线性摄动的状态延迟系统的H∞鲁棒控制

研究了带非线性摄动的状态延迟系统的H∞鲁棒控制.该摄动用有界范数描述,它 不仅与非延迟状态有关,而且与延迟状态有关.用动态耗散理论,基于矩阵不等式,给出了系 统满足H∞鲁棒扰动衰减性能准则的充分条件;同时系统地推导出了独立于延迟的无记忆状 态反馈控制器、基于状态观测器的动态输出反馈控制器和依赖于延迟的状态反馈控制器的设 计算法.     

Near-optimal tracking control for discrete-time systems with delayed input

This paper considers the near-optimal tracking control problem for discrete-time systems with delayed input. Using a variable transformation, the system with delayed input is transformed into a non-delayed system, and the quadratic performance index of the optimal tracking control is transformed into a relevant format. The optimal tracking control law is constructed by the solution of a Riccati matrix equation and a Stein matrix equation. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator and a near-optimal tracking control is obtained. Simulation results demonstrate the effectiveness of the optimal tracking control law.     

Dynamic pricing of durable products with heterogeneous customers and demand interactions over time

In this study, we analyze a dynamic pricing problem in which the demand is interdependent over time and the customers are heterogeneous in their purchasing decisions. The customers are grouped into different classes depending on their purchase probabilities and the customer classes evolve over time depending on the demand realizations at every period, which are a function of the prices set by the company. To decide on the optimal prices at every period, we model this problem using a stochastic dynamic program (SDP) and we develop several approximation algorithms to solve this SDP since the size of the state space of the SDP makes the optimal solution almost impossible to find. We present the efficiencies of the heuristics and provide managerial insights through a computational study in which we compare the revenues obtained with each heuristic with an upper bound value that we find on the optimal revenues.     

Stochastic linear quadratic regulation for discrete-time linear systems with input delay

This paper considers the stochastic LQR problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices. The problem is known to be difficult due to the presence of interactions among the delayed input channels and the stochastic parameter uncertainties in the channels. The key to our approach is to convert the LQR control problem into an optimization one in a Hilbert space for an associated backward stochastic model and then obtain the optimal solution to the stochastic LQR problem by exploiting the dynamic programming approach. Our solution is given in terms of two generalized Riccati difference equations (RDEs) of the same dimension as that of the plant.     

量子粒子群算法在易逝品多目标定价中的应用

对易逝品的多目标定价问题进行了研究。从利润最大化角度建立易逝品多目标最优定价模型。模型中涉及复杂的需求函数,常规函数极值法不易获得问题解析解,因此引入量子粒子群算法,结合惩罚函数对模型进行演化求解。根据给出的算例分析表明,利用量子粒子群算法,可以快速有效地得到不同订货量下的最优定价与折扣价组合。     

Pricing with local interactions on agent-based electronic marketplaces

This paper investigates the optimal pricing strategies of a selling agent that is randomly matched with several heterogeneous buying agents whose reservation prices are initially unknown. The seller perceives the behaviors of the buying agents through a logistic distribution with unknown parameters. We study the optimal learning by experimentation model of the logistic distribution. We extend this framework to a dynamic pricing model in which the selling agent is randomly matched with buying agents that are able to communicate their purchase experience to other buying agents. We carry out multi-agent system simulations of this dynamic pricing decision problem and we discuss some properties of the price dynamics one can observe on such marketplaces.     

A Framework to Determine the Value of Consumer Consideration Set Information for Firm Pricing Strategies

Managers allocating budgets using scarce economic resources increasingly invest in consumer information to set prices. This highlights the importance of developing methods to efficiently use consumer information in firm pricing strategies so as to increase profits. In this article we utilize such a method which includes information about consumer consideration sets. Extant pricing strategies assume that all brands in the market are included in this competitive set while setting prices. Through an empirical illustration in the ketchup market we demonstrate that firms can improve profits substantially by including consumer consideration sets in arriving at their optimal pricing strategies. We find that the ability of a brand to increase prices seems to depend on both the number of competitors it faces as well as the proportion of households for whom there are competitors in their consideration sets. Failure to incorporate consideration sets leads to biased equilibrium margin inferences and a substantial reduction in net profits.     

Fractionally Delayed Kalman Filter

The conventional Kalman filter is based on the assumption of non-delayed measurements. Several modifications appear to address this problem, but they are constrained by two crucial assumptions: 1) the delay is an integer multiple of the sampling interval, and 2) a stochastic model representing the relationship between delayed measurements and a sequence of possible non-delayed measurements is known. Practical problems often fail to satisfy these assumptions, leading to poor estimation accuracy and frequent track-failure. This paper introduces a new variant of the Kalman filter, which is free from the stochastic model requirement and addresses the problem of fractional delay.The proposed algorithm fixes the maximum delay(problem specific), which can be tuned by the practitioners for varying delay possibilities. A sequence of hypothetically defined intermediate instants characterizes fractional delays while maximum likelihood based delay identification could preclude the stochastic model requirement. Fractional delay realization could help in improving estimation accuracy. Moreover, precluding the need of a stochastic model could enhance the practical applicability. A comparative analysis with ordinary Kalman filter shows the high estimation accuracy of the proposed method in the presence of delay.     

Dynamic ordering and pricing for a perishable goods supply chain

The paper studies the combined problem of pricing and ordering for a perishable product supply chain with one supplier and one retailer in a finite horizon. The lifetime of the product is two periods and demand in each period is random and price-sensitive. In each period, the supplier determines first a wholesale price and then the retailer decides an order quantity and retail prices. We show that the optimal pricing strategy for the non-fresh product depends only on its inventory, and the optimal pricing strategy and the optimal order quantity for the fresh product depend only on the wholesale price and they have a constant relation. Moreover, the game between the retailer and the supplier for finite horizon is equivalent to a one period game with only one order. Thus, the optimal policies are identical at each period. For the additive and multiplicative demands, we further obtain equations to compute the optimal strategies. All of above results are extended into the infinite horizon case and longer lifetime products. Finally, a numerical analysis is given.     

基于线性二次型高斯基准的多变量预测控制技术经济性能评估

由于受控过程参数的漂移及缺乏维护,令采用的控制器性能逐渐降低,需要做经济性能评估,以确保其最佳运行状态.因为目前最小方差评估算法没有考虑控制器的约束条件,对此我们采用线性二次型高斯(linearquadratic Gaussian,LQG)基准的模型预测控制(model predictive control,MPC)双层优化控制结构,将控制和输出的加权值引入上层经济性能指标,通过求解LQG问题获取控制与输出方差关系的离散点集,进一步拟合Pareto最优曲面方程,建立优化命题并求解最优经济指标及设定值.对延迟焦化加热炉的多变量MPC控制进行了性能评估及分析,证明该方法可以改进控制器设计,提高经济效益.     

Optimal software pricing in the presence of piracy and word-of-mouth effect

We develop an analytical model that embeds empirical findings on software diffusion to examine optimal pricing strategies for a spreadsheet software product under coalescing effects of piracy and word-of-mouth through its entire life cycle. We find that the demand of the innovators has the most significant impact on the firm's pricing decision. Our research recommends market skimming pricing strategy if innovators' demand is high and the market penetration pricing strategy is preferred otherwise. Surprisingly, the increase of conversion rate of imitators to buyers never significantly alters the pricing strategy pre-determined by the demand of innovators. Most interestingly, the optimal profit from instituting a two prices policy for a software product with five years lifespan outperforms that from a one price policy by no more than 4%, a finding that corroborates the common one price policy observed in reality.     

Capital injections with negative surplus and delays: models and analysis

This work develops a new model to deal with the scenario that some companies can still run business even the surplus falls below zero temporarily. With such a scenario in mind, we allow the surplus process to continue in this negative-surplus period, during which capital injections will be ordered to assist in the stabilization of financial structure, until the financial status becomes severe enough to file bankruptcy. The capital injections will be modeled as impulse controls. By introducing the capital injections with time delays, optimal dividend payment and capital injection policies are considered. Using the dynamic programming approach, the value function obeys a quasi-variational inequality. With delays in capital injections, the company will be exposed to the risk of bankruptcy during the delay period. In addition, the optimal dividend payment and capital injection strategies should balance the expected cost of the possible capital injections and the time value of the delay periods. This gives rise to a stochastic control problem with mixed singular and delayed impulse controls. Under general assumptions, the lower capital injection barrier is determined, where bankruptcy occurs. The closed-form solution to the value function and corresponding optimal policies are obtained.     

Microarchitectures for Managing Chip Revenues under Process Variations

As transistor feature sizes continue to shrink into the sub-90 nm range and beyond, the effects of process variations on critical path delay and chip yields have amplified. A common concept to remedy the effects of variation is speed-binning, by which chips from a single batch are rated by a discrete range of frequencies and sold at different prices. In this paper, we discuss strategies to modify the number of chips in different bins and hence enhance the profits obtained from them. Particularly, we propose a scheme that introduces a small Substitute Cache associated with each cache way to replicate the data elements that will be stored in the high latency lines. Assuming a fixed pricing model, this method increases the revenue by as much as 13.8% without any impact on the performance of the chips.     

Multitask learning and nonlinear optimal control of the COVID-19 outbreak: A geometric programming approach

We propose a multitask learning approach to learn the parameters of a compartmental discrete-time epidemic model from various data sources and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of the model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on individuals’ mobility patterns specific to each region. Using this model, we propose a nonlinear optimal control problem aiming to find the optimal mobility-based intervention strategy that curbs the spread of the epidemic while obeying a budget on the economic cost incurred. We also show that the solution to this nonlinear optimal control problem can be efficiently found, in polynomial time, using tools from geometric programming. Furthermore, in the absence of a straightforward mapping from human mobility data to economic costs, we propose a practical method by which a budget on economic losses incurred may be chosen to eliminate excess deaths due to over-utilization of hospital resources. Our results are demonstrated with numerical simulations using real data from the COVID-19 pandemic in the Philadelphia metropolitan area.     

A QoS-based dynamic pricing approach for services provisioning in heterogeneous wireless access networks

In this paper we propose a simple QoS-based dynamic pricing approach for services provisioning in a heterogeneous wireless access network environment which attempts to increase user’s satisfaction level by firstly, maximizing the provided QoS level, and secondly, by applying dynamic pricing strategies according to the QoS. These strategies will allow service providers to maximize their profits. Simulation results demonstrate that the proposed dynamic pricing approach benefits both users and wireless service providers (WSPs). Results also suggest that users have better overall satisfaction due to a better QoS level and fairer prices. The analysis shows that our proposed pricing approach contributes to an increase in WSPs profits compared to the application of the flat-rate pricing model in a competitive market-model.     

The effects of decision timing for pricing and marketing efforts in a supply chain with competing manufacturers

This paper investigates the impact of decision timing for pricing and marketing efforts in a supply chain led by competing manufacturers. We develop and solve six games to consider the scenarios (games) where prices and marketing efforts (ME) are decided simultaneously, and when they are not (i.e., ME is set either before or after prices). We examine these three scenarios for the benchmark case of a bilateral monopolistic channel, then extend the analysis to a supply chain with competing manufacturers. We identify the optimal decision timing by comparing equilibrium profits and strategies across games in each supply chain setup. We find that a monopolistic manufacturer always prefers that prices and ME be decided simultaneously. However, this result does not hold when product competition is taken into account. The optimal decision timing for competing manufacturers depends on the retailer's and manufacturers' ME effectiveness levels as well as on competition intensity. Specifically, when ME are not very effective, a simultaneous decision scenario is preferred because it provides the advantage of higher profit margins or sales. However, for highly effective ME, manufacturers prefer to decouple ME and pricing decisions. The retailer's optimal scenario is either to make all decisions simultaneously or to choose prices prior to ME. This means that supply chain firms can face conflict due to the decision timing for prices and ME.     

Dynamic Pricing on the Internet: Theory and Simulations

As is the case with traditional markets, the sellers on the Internet do not usually know the demand functions of their customers. However, in such a digital environment, a seller can experiment different prices in order to maximize his profits. In this paper, we fit the dynamic pricing model of Rothschild (1974) to match the pricing problem of a Web-store. In this setting, we define the optimization problem of a Web-store and by simulations we study the price dynamics that can appear when all the sellers on a given market follow an optimal pricing policy.     

Robust optimal control of time‐delay systems based on Razumikhin theorem

This paper presents an optimal control approach for the general robust control design problem of linear time delay systems, which considers parameter uncertainties as well as state delay. It is shown that the robust control problem can be transformed into an optimal control problem with the amouof plant uncertainties involved in the performance index. A stability criterion has been developed under which the uncertain dynamical system can not only achieve stability, but also acquire the guaranteed level of performance for regulation. A suitable linear state feedback control law is also characterized via Lyapunov stability theory to ensure performance robustness of the closed‐loop system. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

The impact of consumer behavior on preannounced pricing for a dual‐channel supply chain

This study discusses a dual‐channel supply chain in which a manufacturer sells a regular‐priced product through dual channels in the normal sales period and only sells overstocked products through the direct channel in the discounted sales period in the presence of strategic consumers. The manufacturer acts as a Stackelberg leader to adopt a preannounced pricing policy. This study first proposes demand functions for a two‐period dual‐channel model by incorporating consumer utility functions. Based on the demand functions, optimal pricing strategies for both manufacturer and retailer are established. The results show that the manufacturer prefers to raise prices in both periods for consumers with a short delivery lead time. However, counterintuitively, the selling prices set by the manufacturer do not decrease as the degree of consumer patience increases. Finally, there is a Pareto zone under a certain condition where both the manufacturer and the retailer in the two‐period dual‐channel model outperform their counterparts in terms of profit in the single‐period dual‐channel model.     

Optimal business process deployment cost in cloud resources

Cloud computing is the fastest emerging technology that proposes several resources under various pricing strategies that are specified based on temporal constraints. The main aim of cloud computing is to enhance the performance level and minimize operating costs. Thus, organizations looking towards optimizing their spending on IT infrastructure find such pricing strategies very attractive, especially, to deploy their business process models. However, discovering the optimal deployment cost of a business process in cloud resources proposed under various pricing strategies becomes a highly challenging problem. So, the objective of the present paper is to present an approach that assists business process designers in finding an optimal assignment or scheduling based on the variety of pricing strategies. We use linear programming models with an objective function under a set of constraints. Besides, we propose an extension of the famous cloud simulator provided in the market, CloudSim, to simulate the cloud resources consumed to deploy a business process model. The experimental results show the feasibility, effectiveness, and performance of our approach.