Feedback stabilization of multi-DOF nonlinear stochastic Markovian jump systems
Feedback stabilization of multi-DOF nonlinear stochastic Markovian jump systems
复制标题
多自由度非线性随机马尔可夫跳跃系统的反馈稳定
DOI：
10.1002/rnc.4689
复制
发表时间：
2019
影响因子：
3.9
通讯作者：
Deng Zichen
中科院分区：
文献类型：
--
作者：
Hu Rongchun;Dong Hao;Gu Xudong;Deng Zichen
反馈控制策略旨在渐近稳定经历马尔可夫跳跃的多自由度（DOF）非线性随机系统。首先，将一类具有马尔可夫跳跃的混合非线性随机系统简化为受控总能量的一维平均 Itô 随机微分方程。其次，将动态规划原理应用于成本函数未定的平均系统的遍历控制问题，推导出最优控制律。第三，成本函数是根据稳定平均系统的要求来确定的。引入李亚普诺夫指数来近似分析原始控制系统概率为一的渐近稳定性。为了说明本方法的应用，详细给出了具有马尔可夫跳跃的随机激励两个耦合非线性振荡器的示例。
A feedback control strategy is designed to asymptotically stabilize a multi‐degree‐of‐freedom (DOF) nonlinear stochastic systems undergoing Markovian jumps. First, a class of hybrid nonlinear stochastic systems with Markovian jumps is reduced to a one‐dimensional averaged Itô stochastic differential equation for controlled total energy. Second, the optimal control law is deduced by applying the dynamical programming principle to the ergodic control problem of the averaged systems with an undetermined cost function. Third, the cost function is determined by the demand of stabilizing the averaged systems. A Lyapunov exponent is introduced to analyze approximately the asymptotic stability with probability one of the originally controlled systems. To illustrate the application of the present method, an example of stochastically excited two coupled nonlinear oscillators with Markovian jumps is worked out in detail.