Farazmand Mohammad
Department of Mathematics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina 27695-8205, USA.
Chaos. 2020 Jan;30(1):013149. doi: 10.1063/1.5137825.
In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria are possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the system stays near a desirable equilibrium. For small delays, we show that the control term has two effects: (i) a stabilizing effect by deepening the potential well around the desirable equilibrium and (ii) a destabilizing effect by intensifying the noise by a factor of (1-τα), where τ and α denote the delay and the control gain, respectively. As a result, successful mitigation depends on the competition between these two factors. We also derive analytical results that elucidate the choice of the appropriate control gain and delay that ensure successful mitigations. These results eliminate the need for any Monte Carlo simulations of the stochastic differential equations and, therefore, significantly reduce the computational cost of determining the suitable control parameters. We demonstrate the application of our results on two examples.
在由势梯度驱动的随机多稳态系统中，由于噪声的存在，平衡点之间的转变是可能的。我们研究线性延迟反馈控制减轻这些转变的能力，以确保系统保持在期望的平衡点附近。对于小延迟，我们表明控制项有两个作用：（i）通过加深期望平衡点周围的势阱产生稳定作用；（ii）通过将噪声增强（1 - τα）倍产生不稳定作用，其中τ和α分别表示延迟和控制增益。因此，成功的减轻取决于这两个因素之间的竞争。我们还推导了分析结果，阐明了确保成功减轻的合适控制增益和延迟的选择。这些结果消除了对随机微分方程进行任何蒙特卡罗模拟的需要，从而显著降低了确定合适控制参数的计算成本。我们在两个例子中展示了我们结果的应用。
