双重时间尺度渐近模拟的混合包含及其在随机混合优化中的应用
Two-Timescale Asymptotic Simulations of Hybrid Inclusions with Applications to Stochastic Hybrid Optimization
AI总结：
本文研究了混合包含的双重时间尺度渐近模拟的收敛性，提出了基于连续和离散动态的混合包含模型，并探讨了其在随机混合优化中的应用条件。
摘要：
模型无关的双重时间尺度渐近模拟的收敛性质被开发，用于奇异摄动的混合包含。混合包含结合了受约束的微分和差分包含，分别捕捉连续（流）和离散（跃迁）动态。建立了充分条件，使得迭代序列和步长构成此类系统的双重时间尺度渐近模拟，其极限行为通过相关边界层和简化系统的弱不变和内部链传递集来表征。为了说明这些结果的适用性，给出了在何种条件下，双重时间尺度随机逼近的混合优化算法渐近恢复其确定性对应体的行为。
英文摘要：
Convergence properties of model-free two-timescale asymptotic simulations of singularly perturbed hybrid inclusions are developed. A hybrid inclusion combines constrained differential and difference inclusions to capture continuous (flow) and discrete (jump) dynamics, respectively. Sufficient conditions are established under which sequences of iterates and step sizes constitute a two-timescale asymptotic simulation of such a system, with limiting behavior characterized via weakly invariant and internally chain-transitive sets of an associated boundary layer and reduced system. To illustrate the applicability of these results, conditions are given under which a two-timescale stochastic approximation of a hybrid optimization algorithm asymptotically recovers the behavior of its deterministic counterpart.
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