King P. E., Yim S. C. S.
U.S. Bureau of Mines, Albany Research Center, Albany, Oregon 97321.
Chaos. 1997 Jun;7(2):290-300. doi: 10.1063/1.166228.
In this study we examine the complex and chaotic oscillations of a dynamical system with nonlinear excitation and restoring forces for the purpose of controlling these oscillatory states. The physical system, modeled as a system of first-order nonlinear ordinary differential equations, takes into account a geometric nonlinearity in the restoring force, a quadratic viscous drag, and a harmonic excitation force. It is controlled using small perturbations about a selected unstable cycle and control is instigated for periodic cycles of varying periodicities. The controller, when applied on the dynamical system with additive random noise in the excitation, successfully controls the system with noise levels in excess of 5% of the total energy, giving the first evidence that (stochastic) control of these systems is possible. (c) 1997 American Institute of Physics.
在本研究中，我们研究了一个具有非线性激励和恢复力的动力系统的复杂混沌振荡，目的是控制这些振荡状态。该物理系统被建模为一阶非线性常微分方程组，考虑了恢复力中的几何非线性、二次粘性阻力和谐波激励力。它通过围绕选定的不稳定周期的小扰动进行控制，并针对不同周期的周期循环进行控制。当该控制器应用于激励中带有加性随机噪声的动力系统时，成功地控制了噪声水平超过总能量5%的系统，首次证明了对这些系统进行（随机）控制是可能的。（c）1997美国物理研究所。
