论文标题
计算混合孔酮系统的稳健前向不变集
Computing Robustly Forward Invariant Sets for Mixed-Monotone Systems
论文作者
论文摘要
这项工作介绍了研究可达到性的新工具，并设定了经受干扰输入的连续时间混合键盘动力学系统的不变性。混合单酮系统的矢量场可以通过分解函数分解成增加和减少组件，并且该分解可以使原始动力学嵌入更高维的嵌入系统中。虽然原始系统受到未知的干扰输入的约束，但嵌入系统没有干扰，其轨迹为有限的时间到达原始动力学集合提供了界限。我们的主要贡献是展示如何通过研究这种嵌入系统的某些均衡来有效地识别混合孔酮系统的稳健前进且有吸引力的集合。我们还展示了这种方法如何应用于向后的动力学时，如何为原始动力学建立不同的稳健前向不变集。最后，我们为计算具有多项式动力学的系统计算分解函数提供了独立的结果。这些工具和结果通过几个示例和案例研究来证明。
This work presents new tools for studying reachability and set invariance for continuous-time mixed-monotone dynamical systems subject to a disturbance input. The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing and decreasing components, and this decomposition enables embedding the original dynamics in a higher-dimensional embedding system. While the original system is subject to an unknown disturbance input, the embedding system has no disturbances and its trajectories provide bounds for finite-time reachable sets of the original dynamics. Our main contribution is to show how one can efficiently identify robustly forward invariant and attractive sets for mixed-monotone systems by studying certain equilibria of this embedding system. We show also how this approach, when applied to the backward-time dynamics, establishes different robustly forward invariant sets for the original dynamics. Lastly, we present an independent result for computing decomposition functions for systems with polynomial dynamics. These tools and results are demonstrated through several examples and a case study.
