论文标题
随机杂种夹杂物的稳定性分析
Stability Analysis for Stochastic Hybrid Inclusions
论文作者
论文摘要
随机杂种夹杂物（SHIS）与随机差异夹杂物中的随机连续演变有关，并且由于强制（在状态空间中达到边界的状态）和/或自发（状态矢量可能会自发发生）过渡引起的差异（状态）引起的差异差异。 SHIS的一个明显特征是随机溶液的非唯一性，可以通过轻度的规律条件以及名义鲁棒性来确保。 Basic sufficient conditions for stability/recurrence in probability are usually expressed based on different types of Lyapunov functions, including Lagrange/Lyapunov/Lyapunov-Forster functions respectively for Lagrange/Lyapunov/asymptotical stability in probability and Foster/Lagrange-Forster functions for recurrence, (weaker) relaxed Lyapunov-based sufficient conditions including Matrosov-Foster functions and the stochastic不变性原理以及基于lyapunov的概率或复发性渐近稳定性的必要条件（即相反定理）等。涉及光滑lyapunov函数的匡威定理由顺序的紧凑性和稳健性保证。另外，分析了概率稳定性的均匀性和因果关系。因此，作为SHIS理论发展的部分路线图（也是灵感），我们预计将根据SHIS的技术来解决许多开放问题，包括预测问题，过滤问题和控制问题。
Stochastic hybrid inclusions (SHIs) address situations with the stochastic continuous evolution in a stochastic differential inclusions and random jumps in the difference inclusions due to the forced (the state reaching a boundary in the state space) and/or spontaneous (the state vector may occur spontaneously) transitions. An obvious characteristic of SHIs is the non-uniqueness of random solutions, which can be ensured by the mild regularity conditions, as well as nominal robustness. Basic sufficient conditions for stability/recurrence in probability are usually expressed based on different types of Lyapunov functions, including Lagrange/Lyapunov/Lyapunov-Forster functions respectively for Lagrange/Lyapunov/asymptotical stability in probability and Foster/Lagrange-Forster functions for recurrence, (weaker) relaxed Lyapunov-based sufficient conditions including Matrosov-Foster functions and the stochastic invariance principle, as well as Lyapunov-based necessary and sufficient conditions for asymptotical stability in probability or recurrence (i.e.,converse theorems), etc. The converse theorems involving smooth Lyapunov functions are guaranteed by the sequential compactness and thus robustness. In addition, the uniformity property and causality are analyzed for the stabilities in probability. Hence, serving as a partial roadmap for the theoretical development of SHIs, also serving as inspiration, we anticipate that many of the open questions, including the prediction problem, the filtering problem and the control problem, will be resolved based on the techniques of SHIs.
