Chaos control in lateral oscillations of spinning disk via linear optimal control of discrete systems

Abstract

Chaos control of a spinning disk having transverse vibration is considered in this article by stabilizing the system on its corresponding unstable periodic orbit (UPO). At the first step, the system continuous-time dynamic equations are quantized by utilizing a proper Poincare map. Then, using the regression method a linear description from the obtained cross points is achieved around the corresponding fixed point of the target UPO. Finally, through solving the Riccati equation, an optimal controller is introduced which stabilizes the system on its unstable fixed point. At the end, the effectiveness of the proposed control method is examined through numerical simulations.

NON‐PDC Observer‐Based T‐S Fuzzy Tracking Controller Design and its Application in CHAOS Control

“…It is worth noting that in the proposed observer‐based control algorithm, we assume all states are not available. However, in , as the only existing works in stabilizing UPOs of chaotic spinning disk model in the literature, complete state information is assumed for the feedback to be used in the control signal.…”

Master-slave synchronization in the van der Pol and Duffing systems via elastic, dissipative and a combination of both couplings

“…The control of chaos is concerned with using some designed control to modify the characteristics of a nonlinear system. A number of methods such as active control, adaptive control, optimal control and sliding mode control exist for the control of chaos in systems Chekan et al (2017), Huang and Cao (2017), Pai (2020), Ye et al (2018). Various kinds of synchronization play a very important role such as phase synchronization, anticipated synchronization, generalized synchronization, projective synchronization, complete synchronization, hybrid synchronization, antisynchronization, multimodal synchronization, forced synchronization, itinerary synchronization and hybrid function projective synchronization have been developed and are frequently used Anzo-Hernández et al (2019), Campos et al (2004), Gonzalez-Salas et al (2008, Khan and Shikha (2017), Ouannas et al (2017), Razminia and Dumitru (2013), Yan and Li (2005).…”

Master-slave synchronization in the Rayleigh and Duffing oscillators via elastic and dissipative couplings

“…The control of chaos is concerned with using some designed control to modify the characteristics of a nonlinear system. A number of methods such as active control, adaptive control, optimal control and sliding mode control exist for the control of chaos in systems [10][11][12][13]. Several kinds of synchronization play an important role in the study of chaos such as phase synchronization, anticipated synchronization, generalized synchronization, projective synchronization, that have been studied and applied to a chaotic and unified system by J. Yan et.…”