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Piecewise-linear H-infinity controller synthesis with applications to inventory control of switched production systems

机译：分段线性H-∞控制器综合及其在切换生产系统的库存控制中的应用

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摘要

This paper focuses on the problem of inventory control of production systems. The main contribution of the paper is that production systems are modeled as constrained switched linear systems and the inventory control problem is formulated as a constrained switched H-infinity problem with a piecewise-affine (PWA) control law. The switching variable for the production systems modeled in this paper is the stock level. When the stock level is positive, some of the perishable produced parts are being stored and will deteriorate with time at a given rate. When the stock level is negative it leads to backorders, which means that orders for production of parts are coming in and there are no stocked parts to immediately meet the demand. A state feedback controller that forces the stock level to be kept close to zero (sometimes called a just-in-time policy), even when there are fluctuations in the demand, will be designed in this paper using H-infinity control theory. The synthesis of the state feedback controller that quadratically stabilizes the production dynamics and at the same time rejects the external demand fluctuation (treated as a disturbance) is cast as a set of linear matrix inequalities (LMIs). Two numerical examples are provided to show the effectiveness of the proposed method. (c) 2006 Elsevier Ltd. All rights reserved.
机译：本文重点讨论生产系统的库存控制问题。本文的主要贡献在于，将生产系统建模为约束切换线性系统，并将库存控制问题表述为具有分段仿射（PWA）控制律的约束切换H-无穷大问题。本文建模的生产系统的转换变量是库存水平。当库存水平为正时，一些易腐坏的生产零件将被存储，并且会随着时间的推移以给定的速度恶化。当库存水平为负时，这将导致缺货，这意味着零件生产订单即将到来，并且没有库存的零件可以立即满足需求。本文将使用H-无穷大控制理论设计一种状态反馈控制器，该控制器可将库存水平保持在接近零的水平（有时称为即时策略），即使需求有波动也是如此。状态反馈控制器的综合可稳定生产动态，同时抑制外部需求波动（被视为干扰），将其转换为一组线性矩阵不等式（LMI）。提供了两个数值示例，说明了该方法的有效性。 （c）2006 Elsevier Ltd.保留所有权利。

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