Rouen Normandie University-CORIA, Avenue de l'Université, F-76800 Saint-Etienne du Rouvray, France.
QUARTZ EA7393 Laboratory, ENSEA, 6 Avenue du Ponceau, 95014 Cergy-Pontoise, France.
Chaos. 2021 Oct;31(10):103114. doi: 10.1063/5.0055895.
Controlling chaotic systems is very often investigated by using empirical laws, without taking advantage of the structure of the governing equations. There are two concepts, observability and controllability, which are inherited from control theory, for selecting the best placement of sensors and actuators. These two concepts can be combined (extended) into flatness, which provides the conditions to fulfill for designing a feedback linearization or another classical control law for which the system is always fully observable and fully controllable. We here design feedback linearization control laws using flatness for the three popular chaotic systems, namely, the Rössler, the driven van der Pol, and the Hénon-Heiles systems. As developed during the last two decades for observability, symbolic controllability coefficients and symbolic flatness coefficients are introduced here and their meanings are tested with numerical simulations. We show that the control law works for every initial condition when the symbolic flatness coefficient is equal to 1.
控制混沌系统通常通过使用经验法则进行研究，而不利用控制方程的结构。有两个概念，可观测性和可控性，它们继承自控制理论，用于选择传感器和执行器的最佳放置位置。这两个概念可以结合（扩展）成平坦度，为设计反馈线性化或其他经典控制律提供了条件，系统总是完全可观测和完全可控的。我们在这里使用平坦度为三个流行的混沌系统（即罗瑟勒、驱动范德波尔和亨尼-海莱系统）设计反馈线性化控制律。正如过去二十年中为可观测性发展的那样，本文引入了符号可控系数和符号平坦度系数，并通过数值模拟测试了它们的含义。我们表明，当符号平坦度系数等于 1 时，控制律适用于每个初始条件。
