Rouen Normandie University-CORIA, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France.
Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-IRD-INRAe, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France.
Chaos. 2023 Jan;33(1):013140. doi: 10.1063/5.0128471.
Controlling chaos is fundamental in many applications, and for this reason, many techniques have been proposed to address this problem. Here, we propose a strategy based on an optimal placement of the sensor and actuator providing global observability of the state space and global controllability to any desired state. The first of these two conditions enables the derivation of a model of the system by using a global modeling technique. In turn, this permits the use of feedback linearization for designing the control law based on the equations of the obtained model and providing a zero-flat system. The procedure is applied to three case studies, including two piecewise linear circuits, namely, the Carroll circuit and the Chua circuit whose governing equations are approximated by a continuous global model. The sensitivity of the procedure to the time constant of the dynamics is also discussed.
控制混沌在许多应用中是基础，出于这个原因，已经提出了许多技术来解决这个问题。在这里，我们提出了一种基于传感器和执行器的最佳放置的策略，该策略提供了状态空间的全局可观测性和对任何期望状态的全局可控性。这两个条件中的第一个可以通过使用全局建模技术来推导出系统的模型。反过来，这允许使用反馈线性化来基于获得的模型的方程设计控制律，并提供零平坦系统。该过程应用于三个案例研究，包括两个分段线性电路，即卡罗尔电路和蔡氏电路，其控制方程由连续全局模型近似。还讨论了该过程对动力学时间常数的敏感性。
