混合动力系统的解与可达集：半连续依赖于初始条件、时间和扰动
Solutions and Reachable Sets of Hybrid Dynamical Systems: Semicontinuous Dependence on Initial Conditions, Time, and Perturbations
摘要：
在轻度正则性约束下，混合系统的序列紧性保证了解对初始条件和扰动的外/上连续依赖性。对于混合系统的可达集，这一性质导致上连续依赖于初始条件，时间和扰动。受这些结果的启发，我们定义了一个对应的序列紧性，并表明它导致较低的连续依赖的初始条件和扰动的解决方案。在续集中，它表明，在适当的假设下，具有这种新的属性的系统的可达集依赖于较低的初始条件，时间和扰动。当这些假设失败时，可达集的连续近似仍然是可能的。引入属性的充要条件由几何约束、正则性假设和切向条件的组合给出。进一步的应用混合系统的模拟和最优控制进行了讨论。
英文摘要：
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property leads to upper semicontinuous dependence with respect to initial conditions, time, and perturbations. Motivated by these results, we define a counterpart to sequential compactness and show that it leads to lower semicontinuous dependence of solutions on initial conditions and perturbations. In the sequel, it is shown that under appropriate assumptions, reachable sets of systems possessing this novel property depend lower semicontinuously on initial conditions, time, and perturbations. When those assumptions fail, continuous approximations of reachable sets turn out to be still possible. Necessary and sufficient conditions for the introduced property are given by a combination of geometric constraints, regularity assumptions, and tangentiality conditions. Further applications to simulations and optimal control of hybrid systems are discussed.
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