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首页> 外文期刊>International journal of systems science >Probabilistic tracking control of dissipated Hamiltonian systems excited by Gaussian white noises
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Probabilistic tracking control of dissipated Hamiltonian systems excited by Gaussian white noises

机译：高斯白噪声激发散热哈密顿系统的概率跟踪控制

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This paper devotes to a feedback control strategy for nonlinear stochastic dynamical system to track a prespecified stationary response probability density. The system description and control design are conducted in Hamiltonian framework, and the excitations are confined to Gaussian white noises. The control design consists of several successive steps: firstly, separating the control into conservative and dissipative components by physical intuition, and expanding two components as polynomials; secondly, deriving the low-dimensional averaged equations of controlled Hamiltonian by stochastic averaging, and obtaining the stationary probability density of controlled responses by solving the associated Fokker-Planck-Kolmogorov (FPK) equation; thirdly and finally, determining the polynomial coefficients by minimising the performance index which balances the tracking performance and control cost. Two examples, i.e. Duffing oscillator and frictional system are adopted to illustrate the application and efficacy of this control strategy to track Gaussian and non-Gaussian response probability density.
机译：本文致力于非线性随机动力系统的反馈控制策略，以跟踪预先限定的静止响应概率密度。系统描述和控制设计在哈密顿框架中进行，激励被限制在高斯白噪声中。控制设计由几个连续步骤组成：首先，通过物理直觉将控制分离为保守和耗散组分，并将两个组件扩展为多项式;其次，通过随机平均来源通过随机平均来通过求解相关的FOKKER-PLANCK-KOLMOGOROV（FPK）方程来获得受控哈密顿人的低维平均方程，并获得受控响应的静止概率密度;第三，最后，通过最小化平衡跟踪性能和控制成本的性能指标来确定多项式系数。采用了两个示例，即，采用Duffing振荡器和摩擦系统来说明该控制策略跟踪高斯和非高斯响应概率密度的应用和功效。

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