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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.

In this article by introducing and subsequently applying the Min–Max method, chaos has been suppressed in discrete time systems. By using this nonlinear technique, the chaotic behavior of Behrens–Feichtinger model is stabilized on its first and second-order unstable fixed points (UFP) in presence and absence of noise signal. In this step, a comparison has also been carried out among the proposed Min–Max controller and the Pyragas delayed feedback control method. Next, to reduce the computation required for controller design, the clustering method has been introduced as a quantization method in the Min–Max control approach. To improve the performance of the acquired controller through clustering method obtained with the Min–Max method, a linear optimal controller is also introduced and combined with the previously discussed nonlinear control law. The resultant combined controller has been applied on the Henon map and through comparison with both Pyragas controller, and the linear optimal controller alone, its advantages are discussed.

Adaptively controlling and minimizing regret in unknown dynamical systems while controlling the growth of the system state is crucial in real-world applications. In this work, we study the problem of stabilizing and regret minimization of linear dynamical systems with system-level actuator redundancy. We propose an optimism-based algorithm that utilizes the actuator redundancy and the possibility of switching between actuating modes to guarantee the boundedness of the state. This is in contrast to the prior works that may result in an exponential (in system dimension) explosion of the state of the system. We theoretically study the rate at which our algorithm learns a stabilizing controller and prove that it achieves a regret upper bound of O( √ T ).

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