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首页> 外文期刊>International Journal of Control >Mean square stabilisation of complex oscillatory regimes in nonlinear stochastic systems
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Mean square stabilisation of complex oscillatory regimes in nonlinear stochastic systems

机译：非线性随机系统中复杂振动体制的均方稳定

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摘要

A problem of stabilisation of the randomly forced periodic and quasiperiodic modes for nonlinear dynamic systems is considered. For this problem solution, we propose a new theoretical approach to consider these modes as invariant manifolds of the stochastic differential equations with control. The aim of the control is to provide the exponential mean square (EMS) stability for these manifolds. A general method of the stabilisation based on the algebraic criterion of the EMS-stability is elaborated. A constructive technique for the design of the feedback regulators stabilising various types of oscillatory regimes is proposed. A detailed parametric analysis of the problem of the stabilisation for stochastically forced periodic and quasiperiodic modes is given. An illustrative example of stochastic Hopf system is included to demonstrate the effectiveness of the proposed technique.
机译：考虑了非线性动态系统的随机强迫周期和拟周期模的稳定问题。对于此问题的解决方案，我们提出了一种新的理论方法，将这些模式视为带控制的随机微分方程的不变流形。控制的目的是为这些歧管提供指数均方根（EMS）稳定性。阐述了一种基于EMS稳定性代数准则的稳定方法。提出了一种用于稳定各种类型振荡机制的反馈调节器设计的建设性技术。给出了随机强迫周期和准周期模态稳定问题的详细参数分析。随机Hopf系统的说明性示例包括在内，以证明所提出技术的有效性。

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