Stability Preserving Simulations and Bisimulations for Hybrid Systems
Stability Preserving Simulations and Bisimulations for Hybrid Systems
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DOI：
10.1109/tac.2015.2422431
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发表时间：
2015-04
影响因子：
6.8
通讯作者：
P. Prabhakar;G. Dullerud;Mahesh Viswanathan
中科院分区：
文献类型：
--
作者：
P. Prabhakar;G. Dullerud;Mahesh Viswanathan
过程之间的前序和等价关系，如模拟和互模拟，在基于最小化和抽象的离散状态系统模态和时间特性的验证和分析中发挥了核心作用。本文研究了保持稳定的混合系统的预序和等价关系。我们首先表明，相对于参考轨迹的稳定性是不保留的传统概念的互模拟或最近提出的更强的概念与额外的连续性约束。我们介绍了一致连续模拟和互模拟的概念，即模拟和互模拟与一些额外的一致连续性条件的关系，可以用来推理的轨迹的稳定性。最后，我们表明，一致连续模拟和互模拟是广泛流行的，通过重铸许多经典的结果证明稳定的动力系统和混合系统建立一个简单的，显然是稳定的系统，（双）-模拟给定的系统，通过一致连续（双）-模拟的存在。本文还简要讨论了基于本文所建立的基础的一种新的稳定性分析抽象方法。
Pre-orders and equivalence relations between processes, like simulation and bisimulation, have played a central role in the minimization and abstraction based verification and analysis of discrete-state systems for modal and temporal properties. In this paper, we investigate the pre-orders and equivalence relations on hybrid systems which preserve stability. We first show that stability with respect to reference trajectories is not preserved by either the traditional notion of bisimulation or the more recently proposed stronger notions with additional continuity constraints. We introduce the concept of uniformly continuous simulation and bisimulation-namely, simulation and bisimulation with some additional uniform continuity conditions on the relation-that can be used to reason about stability of trajectories. Finally, we show that uniformly continuous simulations and bisimulations are widely prevalent, by recasting many classical results on proving stability of dynamical and hybrid systems as establishing the existence of a simple, obviously stable system that (bi)-simulates the given system through uniformly continuous (bi)-simulations. We also discuss briefly a new abstraction method for stability analysis which is based on the foundations developed in the paper.