Allahverdyan Armen E, Khalafyan Edvard A
Alikhanian National Laboratory, Yerevan Physics Institute, 2 Alikhanian Brothers Street, Yerevan 0036, Armenia.
Cosmology Center, Yerevan State University, 1 A. Manoogian Street, Yerevan 0025, Armenia.
Entropy (Basel). 2022 Jul 24;24(8):1020. doi: 10.3390/e24081020.
Dynamical stabilization processes (homeostasis) are ubiquitous in nature, but the needed energetic resources for their existence have not been studied systematically. Here, we undertake such a study using the famous model of Kapitza's pendulum, which has attracted attention in the context of classical and quantum control. This model is generalized and rendered autonomous, and we show that friction and stored energy stabilize the upper (normally unstable) state of the pendulum. The upper state can be rendered asymptotically stable, yet it does not cost any constant dissipation of energy, and only a transient energy dissipation is needed. Asymptotic stability under a single perturbation does not imply stability with respect to multiple perturbations. For a range of pendulum-controller interactions, there is also a regime where constant energy dissipation is needed for stabilization. Several mechanisms are studied for the decay of dynamically stabilized states.
动态稳定过程（稳态）在自然界中无处不在，但其存在所需的能量资源尚未得到系统研究。在此，我们使用著名的卡皮察摆模型进行此类研究，该模型在经典和量子控制背景下备受关注。我们对该模型进行了推广并使其自治，结果表明摩擦力和存储能量能稳定摆的上（通常不稳定）状态。上状态可变为渐近稳定状态，然而这并不需要任何恒定的能量耗散，仅需短暂的能量耗散。在单次扰动下的渐近稳定性并不意味着在多次扰动下也稳定。对于一系列摆 - 控制器相互作用，还存在一个需要恒定能量耗散来实现稳定的区域。我们研究了动态稳定状态衰减的几种机制。
