当前位置: X-MOL 学术SIAM J. Control Optim. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Geometric Control and Disturbance Decoupling for Fractional Systems
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2020-05-26 , DOI: 10.1137/19m1261493
Fabrizio Padula , Lorenzo Ntogramatzidis , Robert Schmid , Ryan Loxton

SIAM Journal on Control and Optimization, Volume 58, Issue 3, Page 1403-1428, January 2020.
We develop a geometric approach for fractional linear time-invariant systems with Caputo-type derivatives. In particular, we generalize the fundamental notions of invariance and controlled invariance to the fractional setting. We then exploit this new geometric framework to address the disturbance decoupling problem via static pseudostate feedback, with and without stability. Our main contribution is a set of necessary and sufficient conditions for the disturbance decoupling problem that are related to the input-output properties of the closed-loop system, and hence they are applicable not just to Caputo-type derivatives but, more broadly, to any type of fractional system. These results show that, while the conditions for guaranteeing the existence of a decoupling pseudostate feedback remain essentially unchanged, the underlying theoretical framework is substantially different, because the fractional derivative is a nonlocal operator and this property plays a major role in the characterization of the evolution of the pseudostate trajectory. In particular, we show that, unlike the integer case, the infinite-dimensional nature of fractional systems means that feedback control is insufficient to maintain the pseudostate trajectory on a controlled invariant subspace, unless the entire past history of the pseudostate has evolved on that subspace. However, feedforward control can achieve this task under certain necessary and sufficient geometric conditions.


中文翻译:

分数系统的几何控制和干扰解耦

SIAM控制与优化杂志,第58卷,第3期,第1403-1428页,2020年1月。
我们为具有Caputo型导数的分数线性时不变系统开发了一种几何方法。特别是,我们将不变性和受控不变性的基本概念推广到分数设置。然后,我们利用这种新的几何框架,通过具有和不具有稳定性的静态伪状态反馈来解决干扰解耦问题。我们的主要贡献是为干扰解耦问题提供了一组与闭环系统的输入-输出特性相关的必要条件,因此,它们不仅适用于Caputo型导数,而且更广泛地适用于任何类型的分数系统。这些结果表明,尽管保证解耦伪状态反馈存在的条件基本上保持不变,基本的理论框架大不相同,因为分数导数是一个非局部算符,并且此属性在伪状态轨迹演化的表征中起主要作用。特别地,我们表明,与整数情况不同,分数系统的无穷大性质意味着反馈控制不足以维持受控不变子空间上的伪状态轨迹,除非伪状态的整个过去历史在该子空间上演化了。但是,前馈控制可以在某些必要和足够的几何条件下实现此任务。特别是,我们表明,与整数情况不同,分数系统的无穷大性质意味着反馈控制不足以维持受控不变子空间上的伪状态轨迹,除非伪状态的整个过去历史在那个子空间上演化了。但是,前馈控制可以在某些必要和足够的几何条件下实现此任务。特别地,我们表明,与整数情况不同,分数系统的无穷大性质意味着反馈控制不足以维持受控不变子空间上的伪状态轨迹,除非伪状态的整个过去历史在该子空间上演化了。但是,前馈控制可以在某些必要和足够的几何条件下实现此任务。
更新日期:2020-07-23
down
wechat
bug