SENSITIVITY ANALYSIS OF LIMIT-CYCLE OSCILLATING HYBRID SYSTEMS
SENSITIVITY ANALYSIS OF LIMIT-CYCLE OSCILLATING HYBRID SYSTEMS
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DOI：
10.1137/100804632
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发表时间：
2011-01-01
影响因子：
3.1
通讯作者：
Barton, Paul I.
中科院分区：
文献类型：
--
作者：
Khan, Kamil A.;Saxena, Vibhu P.;Barton, Paul I.
发展了极限环振荡混合系统的局部一阶灵敏度分析理论，极限环振荡混合系统是表现出连续状态和离散状态动力学的动力系统，其状态轨迹是封闭的、孤立的和时间周期的。提出了初始条件灵敏度和参数灵敏度的计算方法，以准确地解释离散跃迁时灵敏度的任何跳跃，并利用系统的时间周期性。结果表明，任何极限环振荡混合系统的初始条件灵敏度都可以表示为时间衰减分量和时间周期分量的和，使它们在长时间极限内成为周期分量。提出了一种将参数灵敏度分解为三部分的方法，分别表征参数变化对周期、状态变量幅值和相对相位的影响。本文还介绍了周期、幅值和不同相位的参数灵敏度的计算。在这项工作中开发的方法被应用于特定的模型来说明，包括显示状态变量跳跃的模型。
A theory is developed for local, first-order sensitivity analysis of limit-cycle oscillating hybrid systems, which are dynamical systems exhibiting both continuous-state and discrete-state dynamics whose state trajectories are closed, isolated, and time-periodic. Methods for the computation of initial-condition sensitivities and parametric sensitivities are developed to account exactly for any jumps in the sensitivities at discrete transitions and to exploit the time-periodicity of the system. It is shown that the initial-condition sensitivities of any limit-cycle oscillating hybrid system can be represented as the sum of a time-decaying component and a time-periodic component so that they become periodic in the long-time limit. A method is developed for decomposition of the parametric sensitivities into three parts, characterizing the influence of parameter changes on period, state variable amplitudes, and relative phases, respectively. The computation of parametric sensitivities of period, amplitudes, and different types of phases is also described. The methods developed in this work are applied to particular models for illustration, including models exhibiting state variable jumps.