Stable Set-Valued Integration of Nonlinear Dynamic Systems using Affine Set-Parameterizations
Stable Set-Valued Integration of Nonlinear Dynamic Systems using Affine Set-Parameterizations
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DOI：
10.1137/140976807
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发表时间：
2015-10
期刊：
影响因子：
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通讯作者：
B. Houska;M. E. Villanueva;B. Chachuat
中科院分区：
文献类型：
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作者：
B. Houska;M. E. Villanueva;B. Chachuat
参数常微分方程的许多集值积分算法都是将泰勒级数展开与区间算法或泰勒模型算法相结合。由于包裹效应，使用这些算法计算的解集外壳的直径通常在有限积分范围上发散到无穷大，即使ODE轨迹本身可能是渐近稳定的。本文首先描述了一种新的离散集值积分算法，该算法使用预测验证方法来传播通用仿射集参数化，其图像保证包含ODE解集。充分条件，然后推导出该算法是局部渐近稳定的，在这个意义上说，计算的外壳是保证保持稳定的无限时间范围内，当应用到一个动态系统的附近的局部渐近稳定的周期轨道（或平衡点）。关键要求…
Many set-valued integration algorithms for parametric ordinary differential equations (ODEs) implement a combination of Taylor series expansion with either interval arithmetic or Taylor model arithmetic. Due to the wrapping effect, the diameter of the solution-set enclosures computed with these algorithms typically diverges to infinity on finite integration horizons, even though the ODE trajectories themselves may be asymptotically stable. This paper starts by describing a new discretized set-valued integration algorithm that uses a predictor-validation approach to propagate generic affine set-parameterizations, whose images are guaranteed to enclose the ODE solution set. Sufficient conditions are then derived for this algorithm to be locally asymptotically stable, in the sense that the computed enclosures are guaranteed to remain stable on infinite time horizons when applied to a dynamic system in the neighborhood of a locally asymptotically stable periodic orbit (or equilibrium point). The key requireme...