Tight Decomposition Functions for Continuous-Time Mixed-Monotone Systems With Disturbances
Tight Decomposition Functions for Continuous-Time Mixed-Monotone Systems With Disturbances
复制标题
带扰动的连续时间混合单调系统的紧分解函数
DOI：
10.1109/lcsys.2020.3001085
复制
发表时间：
2020
影响因子：
3
通讯作者：
S. Coogan
中科院分区：
文献类型：
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作者：
Matthew Abate;Maxence Dutreix;S. Coogan
混合单调系统的向量场可通过分解函数分解为递增（合作）和递减（竞争）分量，这种分解使得可达集和前向不变集的高效计算成为可能。然而，这种方法的主要挑战是确定适当的分解函数。在这篇文章中，我们证明了任何具有Lipschitz连续向量场的连续时间动力系统是混合单调的，并且我们提供了一个分解函数的构造，当使用混合单调系统的标准工具时，它产生了可达集的最紧密逼近。我们的构造类似于Yang和Ozay最近提出的计算离散时间系统分解函数的构造，其中我们对连续时间设置进行了适当的修改，并扩展到具有未知干扰输入的情况。与Yang和Ozay的工作一样，我们的分解函数构造需要为状态空间中的每个点解决一个优化问题；然而，我们通过例子证明了紧密分解函数有时是如何以封闭形式计算的。作为第二个贡献，我们展示了如何通过考虑后向时间动力学，通过混合单调性有效地计算可达集的欠逼近。
The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing (cooperative) and decreasing (competitive) components, and this decomposition allows for, e.g., efficient computation of reachable sets and forward invariant sets. A main challenge in this approach, however, is identifying an appropriate decomposition function. In this letter, we show that any continuous-time dynamical system with a Lipschitz continuous vector field is mixed-monotone, and we provide a construction for the decomposition function that yields the tightest approximation of reachable sets when used with the standard tools for mixed-monotone systems. Our construction is similar to that recently proposed by Yang and Ozay for computing decomposition functions of discrete-time systems where we make appropriate modifications for the continuous-time setting and also extend to the case with unknown disturbance inputs. As in Yang’s and Ozay’s work, our decomposition function construction requires solving an optimization problem for each point in the state-space; however, we demonstrate through example how tight decomposition functions can sometimes be calculated in closed form. As a second contribution, we show how under-approximations of reachable sets can be efficiently computed via the mixed-monotonicity property by considering the backward-time dynamics.
DOI：
--
发表时间：
2019
期刊：
58th IEEE Conference on Decision and Control (CDC
影响因子：
--
作者：
Yang, Liren;Ozay, Necmiye
通讯作者：
Ozay, Necmiye
计算混合单调系统的鲁棒前向不变集
DOI：
--
发表时间：
2020
期刊：
IEEE Conference on Decision and Control
影响因子：
--
作者：
Abate, Matthew;Coogan, Samuel
通讯作者：
Coogan, Samuel