Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems

被引：301

作者：

Abate, Alessandro ^{[1
]}

Prandini, Maria ^{[2
]}

Lygeros, John ^{[3
]}

Sastry, Shankar ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA

[2] Politecn Milan, Dipartimento Elettron & Informaz, Milan, Italy

[3] Swiss Fed Inst Technol, Automat Control Lab, Zurich, Switzerland

来源：

AUTOMATICA | 2008年 / 44卷 / 11期

关键词：

Hybrid systems; Stochastic systems; Reachability; Safety; Optimal control; Dynamic programming;

D O I：

10.1016/j.automatica.2008.03.027

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this work, probabilistic reachability over a finite horizon is investigated for a class of discrete time stochastic hybrid systems with control inputs. A suitable embedding of the reachability problem in a stochastic control framework reveals that it is amenable to two complementary interpretations, leading to dual algorithms for reachability computations. In particular, the set of initial conditions providing a certain probabilistic guarantee that the system will keep evolving within a desired 'safe' region of the state space is characterized in terms of a value function, and 'maximally safe' Markov policies are determined via dynamic programming. These results are of interest not only for safety analysis and design, but also for solving those regulation and stabilization problems that can be reinterpreted as safety problems. The temperature regulation problem presented in the paper as a case study is one such case. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：2724 / 2734

页数：11

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