Title: Frequency-dependent Switching Control for Disturbance Attenuation of Linear Systems Show Chinese title

Title: 基于频率依赖的切换控制用于线性系统扰动衰减

Abstract: The generalized Kalman-Yakubovich-Popov lemma as established by Iwasaki and Hara in 2005 marks a milestone in the analysis and synthesis of linear systems from a finite-frequency perspective. Given a pre-specified frequency band, it allows us to produce passive controllers with excellent in-band disturbance attenuation performance at the expense of some of the out-of-band performance. This paper focuses on control design of linear systems in the presence of disturbances with non-strictly or non-stationary limited frequency spectrum. We first propose a class of frequency-dependent excited energy functions (FD-EEF) as well as frequency-dependent excited power functions (FD-EPF), which possess a desirable frequency-selectiveness property with regard to the in-band and out-of-band excited energy as well as excited power of the system. Based upon a group of frequency-selective passive controllers, we then develop a frequency-dependent switching control (FDSC) scheme that selects the most appropriate controller at runtime. We show that our FDSC scheme is capable to approximate the solid in-band performance while maintaining acceptable out-of-band performance with regard to global time horizons as well as localized time horizons. The method is illustrated by a commonly used benchmark model. Show Chinese abstract

Abstract: 广义Kalman-Yakubovich-Popov引理由Iwasaki和Hara在2005年确立，标志着从有限频率视角分析和综合线性系统的一个里程碑。给定一个预设的频率范围，它允许我们生成具有优良带内干扰抑制性能的无源控制器，代价是牺牲部分带外性能。 本文专注于存在具有非严格或非平稳有限频谱的干扰时线性系统的控制设计。我们首先提出了一类频率相关的激发能量函数（FD-EEF）以及频率相关的激发功率函数（FD-EPF），这些函数针对系统在带内和带外的激发能量及激发功率具有良好的频率选择性属性。 基于一组频率选择性无源控制器，我们随后开发了一种频率相关切换控制（FDSC）方案，在运行时选择最合适的控制器。我们表明，我们的FDSC方案能够在全局时间范围和局部时间范围内保持可接受的带外性能的同时，逼近理想的带内性能。 该方法通过一个常用的基准模型进行了说明。