Exploiting nonlinear invariants and path constraints to achieve tighter reachable set enclosures using differential inequalities
Exploiting nonlinear invariants and path constraints to achieve tighter reachable set enclosures using differential inequalities
复制标题
利用非线性不变量和路径约束，使用微分不等式实现更紧密的可达集包围
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Joseph K. Scott
中科院分区：
文献类型：
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作者：
Kai;Joseph K. Scott
本文提出了一种在非线性动态系统的解决方案上计算急剧界限的新方法，但受到不确定的初始条件，参数和随时间变化的输入。这种界限广泛用于算法中，用于不确定性传播，稳健状态估计，系统验证，全局动态优化等等。最近，已经表明，通过利用已知为所有感兴趣的轨迹（例如，在动态优化的背景下描述可行轨迹的路径约束）所知的状态约束，通常可以通过差异不平等计算的界限来保守得多。明确描述包含所有系统轨迹的不变集的约束。但是，此类有效的边界算法目前仅适用于线性约束的问题。此外，这些算法的基本结果不适用于依赖时间变化输入的约束，并依赖于对非线性约束非常有限的假设。本文贡献了一种新的差异不平等定理，该定理允许使用非常一般的非线性状态约束类别。此外，提出了一种新算法，以有效利用非线性约束以达到更严格的范围。提出的方法显示出对两个具有挑战性的案例研究产生非常尖锐的界限。
This article presents a new method for computing sharp bounds on the solutions of nonlinear dynamic systems subject to uncertain initial conditions, parameters, and time-varying inputs. Such bounds are widely used in algorithms for uncertainty propagation, robust state estimation, system verification, global dynamic optimization, and more. Recently, it has been shown that bounds computed via differential inequalities can often be made much less conservative by exploiting state constraints that are known to hold for all trajectories of interest (e.g., path constraints that describe feasible trajectories in the context of dynamic optimization, or constraints that explicitly describe invariant sets containing all system trajectories). However, effective bounding algorithms of this type are currently only available for problems with linear constraints. Moreover, the theoretical results underlying these algorithms do not apply to constraints that depend on time-varying inputs and rely on assumptions that prove to be very restrictive for nonlinear constraints. This article contributes a new differential inequalities theorem that permits the use of a very general class of nonlinear state constraints. Moreover, a new algorithm is presented for efficiently exploiting nonlinear constraints to achieve tighter bounds. The proposed approach is shown to produce very sharp bounds for two challenging case studies.
影响因子：
1.9
作者：
B. Houska;B. Chachuat
通讯作者：
B. Houska;B. Chachuat
DOI：
10.1137/140976807
发表时间：
2015-10
期刊：
SIAM J. Numer. Anal.
影响因子：
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作者：
B. Houska;M. E. Villanueva;B. Chachuat
通讯作者：
B. Houska;M. E. Villanueva;B. Chachuat