Impulse differential inclusions: a viability approach to hybrid systems

Impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Connections to standard problems in the area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these conditions, methods are developed for approximating their viability and invariance kernels, that is the largest subset that is viable or invariant under the action of the impulse differential inclusion. The results are demonstrated on examples.

[1]  Anna Philippou,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2018, Lecture Notes in Computer Science.

[2]  Bruce H. Krogh,et al.  Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations , 1999, HSCC.

[3]  A. Pnueli,et al.  Effective synthesis of switching controllers for linear systems , 2000, Proceedings of the IEEE.

[4]  Edward Y. Chang,et al.  STeP: The Stanford Temporal Prover , 1995, TAPSOFT.

[5]  P. Saint-Pierre,et al.  Set-Valued Numerical Analysis for Optimal Control and Differential Games , 1999 .

[6]  J. Lygeros,et al.  A game theoretic approach to controller design for hybrid systems , 2000, Proceedings of the IEEE.

[7]  Pravin Varaiya,et al.  Ellipsoidal Techniques for Reachability Analysis , 2000, HSCC.

[8]  P.J. Antsaklis,et al.  Supervisory control of hybrid systems , 2000, Proceedings of the IEEE.

[9]  Stavros Tripakis,et al.  The Tool KRONOS , 1996, Hybrid Systems.

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

[11]  Olivier Bournez,et al.  Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems , 2000, HSCC.

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

[13]  E. Cruck,et al.  Estimation of Basins of Attraction for Uncertain Systems with Affine and Lipschitz Dynamics , 2001 .

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

[15]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

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

[17]  Thomas Brihaye,et al.  On O-Minimal Hybrid Systems , 2004, HSCC.

[18]  A. Nerode,et al.  Logics for hybrid systems , 2000, Proceedings of the IEEE.

[19]  Panos J. Antsaklis,et al.  Special issue on hybrid systems: theory and applications a brief introduction to the theory and applications of hybrid systems , 2000, Proc. IEEE.

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

[21]  Thomas A. Henzinger,et al.  A User Guide to HyTech , 1995, TACAS.

[22]  V. Borkar,et al.  /spl epsiv/-approximation of differential inclusions , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

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

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

[25]  A. Nerode,et al.  Hybrid Control Systems: An Introductory Discussion to the Special Issue , 1998, IEEE Trans. Autom. Control..

[26]  Jean-Pierre Aubin,et al.  Viability theory , 1991 .

[27]  Wang Yi,et al.  UPPAAL - a Tool Suite for Automatic Verification of Real-Time Systems , 1996, Hybrid Systems.

[28]  John Lygeros,et al.  Controlled Invariance of Discrete Time Systems , 2000, HSCC.

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

[30]  Zdzisław Denkowski,et al.  Set-Valued Analysis , 2021 .

[31]  Rajeev Alur,et al.  Timing Analysis in COSPAN , 1996, Hybrid Systems.

[32]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[33]  Stavros Tripakis,et al.  Verification of Hybrid Systems with Linear Differential Inclusions Using Ellipsoidal Approximations , 2000, HSCC.

[34]  Oded Maler,et al.  Reachability Analysis via Face Lifting , 1998, HSCC.

[35]  P. Saint-Pierre.  Approximation of viability kernels and capture basins for hybrid systems , 2001, 2001 European Control Conference (ECC).

[36]  Alain Bensoussan,et al.  Impulse Control and Quasi-Variational Inequalities , 1984 .

[37]  Marc Quincampoix,et al.  Differential inclusions and target problems , 1992 .

[38]  J. M. Schumacher.  Call for papers Automatica special issue on hybrid systems , 1997, Autom..

[39]  S. Sastry,et al.  On the existence of executions of hybrid automata , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[40]  Andrey V. Savkin,et al.  Globally periodic behavior of switched flow networks with a cyclic switching policy , 1999 .

[41]  Ian M. Mitchell,et al.  Integrating Projections , 1998, HSCC.

[42]  Nancy A. Lynch,et al.  Hybrid I/O automata , 1995, Inf. Comput..

[43]  Ian M. Mitchell,et al.  Level Set Methods for Computation in Hybrid Systems , 2000, HSCC.