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A direct method of constructing H{sub}2 suboptimal controllers -Discrete-time systems

机译：一种构建H {SUB} 2次优控制器的直接方法 - 用于时间系统

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For discrete-time systems, an H{sub}2 suboptimal control problem is defined and analyzed. Then an algorithm called 'H{sub}2 suboptimal state feedback gain sequence' (H{sub}2 SOSFGS) algorithm is developed. Rather than utilizing a perturbationmethod' which is numerically stiff and computationally prohibitive, the H{sub}2 SOSFGS algorithm utilizes a direct eigenvalue assignment method to come up with a sequence of H{sub}2 suboptimal state feedback gains. Also, although the sequence of H{sub}2suboptimal state feedback gains constructed by the H{sub}2 SOSFGS algorithm depends on a parameter e, the construction procedure itself does not require explicitly the value of the parameterε. Next, attention is focused on constructing a sequence ofH{sub}2 suboptimal estimator based measurement feedback controllers. Three different estimator structures, prediction, current, and reduced order estimators, are considered. For a given H{sub}2 suboptimal state feedback gain, a sequence of estimator gains for any of the three considered estimators can be constructed by merely dualizing the H{sub}2 SOSFGS algorithm. The direct method of constructing H{sub}2 suboptimal controllers developed here has a number of advantages over the 'perturbation method',e.g., it has the ability to design all three types of estimator based controllers while still maintaining throughout the design the computational simplicity of it.This paper is the discrete-time version of [4]. There are some conceptual similarities as well as fundamental differences between the H{sub}2 suboptimal control problems for continuous- and discrete-time systems. The fundamental differences arise mainlyfrom the fact that, in contrast to continuous-time, for discrete-time systems, the infimum of the H{sub}2 norm over the class of strictly proper controllers is in general different from the infimum of the H{sub}2 norm over the class of proper controllers.
机译：对于离散时间系统，定义和分析了H {Sub} 2次优控制问题。然后，开发了一种称为'h {sub} 2子优化状态反馈增益序列'（h {sub} 2 sosfgs）算法的算法。而不是利用具有数值僵硬和计算禁止的PerturbationMethod'，H {Sub} 2 SOSFGS算法利用直接特征值分配方法来提出一系列H {子} 2次优状态反馈增益。此外，尽管由H {Sub} 2 SOSFGS算法构建的H {Sub} 2的序列2Suboptimal状态反馈增益取决于参数e，但是施工过程本身不需要明确地明确参数的值。接下来，注意力集中在构建基于HOSH {SUB} 2次优估计器的测量反馈控制器的序列。考虑了三种不同的估计结构，预测，电流和减少的订单估计。对于给定的H {子} 2次优状态反馈增益，可以通过仅通过对H {SOU} 2 SOSFGS算法进行两种考虑的估计器中任一项的估计器增益序列。构建H {SUB} 2的直接方法在此开发的次优控制器具有与“扰动方法”相比的许多优点，例如，它具有设计所有三种基于估计器的控制器的控制器，同时仍然在整个设计中保持计算简单性其中。本文是[4]的离散时间版本。对于连续和离散时间系统的H {sub} 2次优控制问题，存在一些概念相似之处以及基本差异。基本差异主要是从与连续时间进行对比的离散时间系统相比，对严格适当的控制器类别的H {sub} 2规范的最小值不同的事实是一般不同于H {在适当的控制器类上的子} 2规范。

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