Dwell Time Refinement

The abstraction of a hybrid system by eliminating one or more of its continuous variables is in general too coarse. In this situation, dwell time refinement may be useful. The idea is to impose explicit constraints on the time that may resp. must be spent (or “dwelled”) between successive mode switches. We show how the required constraints can be inferred automatically (with acceptable cost). The approach is general in that it can be superposed on a range of verification methods for hybrid systems. We exemplify its practical potential by experiments on previously unsolved instances of the stability verification problem.

[1]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[2]  Pravin Varaiya,et al.  Verification of Hybrid Systems Using Abstractions , 1996, Hybrid Systems.

[3]  T. Henzinger,et al.  Algorithmic Analysis of Nonlinear Hybrid Systems , 1998, CAV.

[4]  Pravin Varaiya,et al.  Modeling and verification of hybrid systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[5]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[6]  Thomas A. Henzinger,et al.  HYTECH: a model checker for hybrid systems , 1997, International Journal on Software Tools for Technology Transfer.

[7]  T. Henzinger,et al.  Algorithmic analysis of nonlinear hybrid systems , 1998, IEEE Trans. Autom. Control..

[8]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[9]  Vijay Kumar,et al.  Modular Specification of Hybrid Systems in CHARON , 2000, HSCC.

[10]  O. Stursberg,et al.  On the Generation of Timed Discrete Approximations for Continuous Systems , 2000 .

[11]  Alberto Bemporad,et al.  HYSDEL-a tool for generating computational hybrid models for analysis and synthesis problems , 2004, IEEE Transactions on Control Systems Technology.

[12]  Eugene Asarin,et al.  Abstraction by Projection and Application to Multi-affine Systems , 2004, HSCC.

[13]  Goran Frehse PHAVer: Algorithmic Verification of Hybrid Systems Past HyTech , 2005, HSCC.

[14]  Andreas Podelski,et al.  Model Checking of Hybrid Systems: From Reachability Towards Stability , 2006, HSCC.

[15]  A. Podelski,et al.  A Sound and Complete Proof Rule for Region Stability of Hybrid Systems , 2007, HSCC.

[16]  Sumit Kumar Jha,et al.  Reachability for Linear Hybrid Automata Using Iterative Relaxation Abstraction , 2007, HSCC.

[17]  Andreas Podelski,et al.  Region Stability Proofs for Hybrid Systems , 2007, FORMATS.

[18]  Oded Maler,et al.  Approximating Continuous Systems by Timed Automata , 2008, FMSB.

[19]  Bernd Finkbeiner,et al.  Stability Proofs for Hybrid Systems , 2008 .

[20]  Nancy A. Lynch,et al.  Verifying average dwell time of hybrid systems , 2008, TECS.