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首页> 外文期刊>IEEE Transactions on Automatic Control >Multiple objective optimal control of linear systems: the quadratic norm case
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Multiple objective optimal control of linear systems: the quadratic norm case

机译：线性系统的多目标最优控制：二次范式

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摘要

Control of a linear system to meet requirements embodied in multiple performance criteria is recognized as the typical design problem. The authors study the design of control when every criterion of interest takes the form of an H/sub 2/ norm defined over certain exogenous inputs and controlled outputs of the system. The objective is to find all stabilizing controllers that are noninferior with respect to the defined objectives, that is, to find the set of Pareto-optimal controllers. The novel feature is the use of the Youla parametrization to represent the admissible controllers. This representation enables the authors to show that each criterion, and hence their weighted sum, is convex over the class of admissible controllers. Since the set of admissible controllers is itself convex, the Pareto-optimal controllers can be determined by the standard scalarization technique. It is concluded that, in general, the controller order is higher than the order of the plant.
机译：控制线性系统以满足多种性能标准中体现的要求是公认的典型设计问题。作者研究了当每个感兴趣的标准都采用H / sub 2 /范数形式定义的控制设计，该H / sub 2 /范式定义了系统的某些外部输入和受控输出。目的是找到在定义目标方面不逊于所有稳定控制器，即找到一组帕累托最优控制器。新颖的功能是使用Youla参数化表示可允许的控制器。这种表示使作者能够表明，每个准则及其加权总和在可允许控制器的类别上是凸的。由于可允许控制器的集合本身是凸的，因此可以通过标准的标量技术确定帕累托最优控制器。可以得出结论，一般而言，控制器的顺序高于工厂的顺序。

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