时延混成系统的切换控制器合成  

Switching controller synthesis for time-delayed hybrid systems

作　　者：白云军 甘庭 焦莉 薛白 詹乃军 Yunjun Bai;Ting Gan;Li Jiao;Bai Xue;Naijun Zhan

机构地区：[1]中国科学院大学,中国科学院软件研究所,计算机科学国家重点实验室,北京100190 [2]武汉大学计算机学院,武汉430072

出　　处：《中国科学：数学》2021年第1期97-114,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:61625206,61732001,61872341,61902284和61836005)资助项目。

摘　　要：如何设计安全、可靠的信息物理融合系统是计算机科学和控制理论面临的一个重大挑战.时延现象在信息物理融合系统中普遍存在,时延对系统的稳定性、安全性和控制性能具有实质性影响.但是在已有时延系统验证和控制器合成的工作中往往忽略时延因素,这会导致在不考虑时延情况下能保证稳定和安全的系统在实际运行时因为时延原因而不再稳定和安全.因为时延使得系统的行为演化不仅与当前状态有关,还依赖于系统的历史状态,所以时延混成系统的验证和控制合成更加困难.本文研究信息物理融合系统在考虑时延情形下切换控制器合成问题,提出基于不变式生成技术的控制器合成方法.首先,利用谱分析和线性化技术将时延系统的微分不变式生成问题归结为有界时间的可达集计算问题;然后,提出基于抽象精化的算法计算时延系统有界时间可达集的上近似;最后,实现本文算法并使用实例验证该方法的有效性.How to design safe and reliable safety-critical cyber-physical systems(CPSs)so that we can bet our daily lives on them is a grand challenge to computer science and control theory.Delays in feedback control are ubiquitous,i.e.,the behavior evolution of a system depends not only on its current state,but also on its execution history.Obviously,delays may invalidate the stability/safety certificates obtained by abstracting them away as in the design of modern CPSs normally.In this paper,we study the switching controller synthesis problem of time-delayed hybrid systems,and propose an invariant-based approach by extending the corresponding approach to the design of CPSs without delays.To this end,based on spectral analysis and linearization,we first show that the differential invariant generation problem of delayed dynamical systems can be reduced to computing reachable sets over bounded time horizons;we then propose an abstract-based algorithm to over-approximate the reachable set over a given time bound;finally,we implement a prototypical tool of our approach and illustrate it with examples.

关 键 词：时延混成系统 时延微分方程 微分不变式 切换控制器 安全性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]