Analysis of Zeno behaviors in hybrid systems

We investigate conditions for existence of Zeno behaviors in hybrid systems. Our approach is based on a simple but crucial observation that a state of the hybrid system is reachable at a given time if and only if it is reachable at the same time in an "equivalent" continuous system that is obtained as a suitable weighted combination of the dynamic equations of the hybrid system in the different discrete configurations. Thus, instead of a difficult investigation of the rather complicated class of behaviors of the hybrid system, we examine the very simple class of behaviors of the "equivalent" continuous system.

[1]  Feng Lin,et al.  Synthesis of Minimally Restrictive Legal Controllers for a Class of Hybrid Systems , 1996, Hybrid Systems.

[2]  John Lygeros,et al.  Controllers for reachability specifications for hybrid systems , 1999, Autom..

[3]  Amir Pnueli,et al.  Symbolic Controller Synthesis for Discrete and Timed Systems , 1994, Hybrid Systems.

[4]  Andrey V. Savkin,et al.  Existence and Stability of Periodic Trajectories in Switched Server Systems , 1999 .

[5]  Pravin Varaiya,et al.  What's decidable about hybrid automata? , 1995, STOC '95.

[6]  H. Wong-Toi,et al.  The synthesis of controllers for linear hybrid automata , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[7]  Karl Henrik Johansson,et al.  Dynamical properties of hybrid automata , 2003, IEEE Trans. Autom. Control..

[8]  Karl Henrik Johansson,et al.  Dynamical Systems Revisited: Hybrid Systems with Zeno Executions , 2000, HSCC.

[9]  Thomas A. Henzinger,et al.  Discrete-Time Control for Rectangular Hybrid Automata , 1997, Theor. Comput. Sci..

[10]  Joseph Sifakis,et al.  On the Synthesis of Discrete Controllers for Timed Systems (An Extended Abstract) , 1995, STACS.

[11]  Michael Heymann,et al.  Control of Rate-Bounded Hybrid Systems with Liveness Specifications , 1998 .

[12]  Thomas A. Henzinger,et al.  Using HyTech to Synthesize Control Parameters for a Steam Boiler , 1995, Formal Methods for Industrial Applications.

[13]  A I Bulgakov,et al.  Approximation of differential inclusions , 2002 .

[14]  T. Villa,et al.  Controller synthesis for hybrid systems with lower bounds on event separation , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[15]  Karl Henrik Johansson,et al.  Towards a Geometric Theory of Hybrid Systems , 2000, HSCC.

[16]  S. Sastry,et al.  Zeno hybrid systems , 2001 .

[17]  Andrey V. Savkin,et al.  Existence and stability of periodic trajectories in switched server systems , 2000, Autom..

[18]  Andrey V. Savkin,et al.  Cyclic linear differential automata: a simple class of hybrid dynamical systems , 2000, Autom..

[19]  Pravin Varaiya,et al.  Epsilon-Approximation of Differential Inclusions , 1996, Hybrid Systems.

[20]  M. Egerstedt,et al.  On the regularization of Zeno hybrid automata , 1999 .

[21]  Zohar Manna,et al.  From Timed to Hybrid Systems , 1991, REX Workshop.

[22]  B. Krogh,et al.  Synthesis of supervisory controllers for hybrid systems based on approximating automata , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[23]  Feng Lin,et al.  Control Synthesis for a Class of Hybrid Systems Subject to Configuration-Based Safety Constraints , 1997, HART.

[24]  Feng Lin,et al.  Synthesis and Viability of Minimally Interventive Legal Controllers for Hybrid Systems , 1998, Discret. Event Dyn. Syst..

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

[26]  Deepak Kapur,et al.  Synthesizing Controllers for Hybrid Systems , 1997, HART.

[27]  Thomas A. Henzinger,et al.  Discrete-Time Control for Rectangular Hybrid Automata , 1997, ICALP.