Some decidable results on reachability of solvable systems

ISCAS OpenIR

	Some decidable results on reachability of solvable systems
	Xu, Ming; Zhu, Jiaqi; Li, Zhi-Bin
	2013
发表期刊	INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
ISSN	0308-1079
卷号	42 期号:4 页码:405-425
摘要	Reachability analysis plays an important role in verifying the safety of modern control systems. In the existing work, there are many decidable results on reachability of discrete systems. For continuous systems, however, the known decidable results are established merely for linear systems. In this paper, we propose a class of nonlinear systems (named solvable systems) extending linear systems. We first show that their solutions are of closed form. On the basis of it, we study a series of reachability problems for various subclasses of solvable systems. Our main results are that these reachability problems are decidable by manipulations in number theory, real root isolation, and quantifier elimination. Finally the decision procedures are implemented in a Maple package REACH to solve several non-trivial examples.; Reachability analysis plays an important role in verifying the safety of modern control systems. In the existing work, there are many decidable results on reachability of discrete systems. For continuous systems, however, the known decidable results are established merely for linear systems. In this paper, we propose a class of nonlinear systems (named solvable systems) extending linear systems. We first show that their solutions are of closed form. On the basis of it, we study a series of reachability problems for various subclasses of solvable systems. Our main results are that these reachability problems are decidable by manipulations in number theory, real root isolation, and quantifier elimination. Finally the decision procedures are implemented in a Maple package REACH to solve several non-trivial examples.
收录类别	SCI
关键词	Reachability Analysis Solvable Mappings Nonlinear Systems Hybrid Systems Symbolic Computation Decision Procedures
部门归属	[Xu, Ming; Li, Zhi-Bin] E China Normal Univ, Dept Comp Sci & Technol, Shanghai 200241, Peoples R China. [Xu, Ming; Zhu, Jiaqi] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China.
语种	英语
WOS记录号	WOS:000315676500007
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16937
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Xu, Ming,Zhu, Jiaqi,Li, Zhi-Bin. Some decidable results on reachability of solvable systems[J]. INTERNATIONAL JOURNAL OF GENERAL SYSTEMS,2013,42(4):405-425.
APA	Xu, Ming,Zhu, Jiaqi,&Li, Zhi-Bin.(2013).Some decidable results on reachability of solvable systems.INTERNATIONAL JOURNAL OF GENERAL SYSTEMS,42(4),405-425.
MLA	Xu, Ming,et al."Some decidable results on reachability of solvable systems".INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 42.4(2013):405-425.