Modeling of hybrid systems

The distinguishing characteristic of hybrid systems is the interaction between a continuous-time and a discrete-event component. By modeling these different components using differential equations and finite state automata, it is possible to represent a wide range of phenomena present in physical and technological systems. This paper illustrates hybrid dynamics by several simple examples. Some of these examples illustrate properties of hybrid systems not present in purely continuous or purely discrete systems, while others illustrate application domains such as vehicle control and real-time systems. A mathematical model called a hybrid automaton is then introduced, to show how hybrid dynamics can be formally analyzed.

[1]  Katsuhisa Furuta,et al.  Swinging up a pendulum by energy control , 1996, Autom..

[2]  Jean-Pierre Aubin,et al.  Impulse differential inclusions: a viability approach to hybrid systems , 2002, IEEE Trans. Autom. Control..

[3]  A. Rantzer,et al.  Optimal control of hybrid systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[4]  Mats Andersson,et al.  Object-Oriented Modelling and Simulation , 1993 .

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

[6]  John Lygeros,et al.  A verified hybrid controller for automated vehicles , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

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

[8]  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.

[9]  L. Tavernini.  Differential automata and their discrete simulators , 1987 .

[10]  Thomas A. Henzinger,et al.  Modularity for Timed and Hybrid Systems , 1997, CONCUR.

[11]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

[12]  S. Shankar Sastry,et al.  Conflict resolution for air traffic management: a study in multiagent hybrid systems , 1998, IEEE Trans. Autom. Control..

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

[14]  Hilding Elmqvist,et al.  Modelica hybrid modeling and efficient simulation , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[15]  A. J. van der Schaft,et al.  Complementarity modeling of hybrid systems , 1998, IEEE Trans. Autom. Control..

[16]  W. P. M. H. Heemels,et al.  Linear Complementarity Systems , 2000, SIAM J. Appl. Math..

[17]  J. C. Clegg.  A nonlinear integrator for servomechanisms , 1958, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[18]  Akash Deshpande,et al.  The SHIFT programming language for dynamic networks of hybrid automata , 1998 .

[19]  Pravin Varaiya,et al.  Smart cars on smart roads: problems of control , 1991, IEEE Trans. Autom. Control..

[20]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[21]  J. M. Schumacher,et al.  Compositionality issues in discrete, continuous, and hybrid systems , 2001 .

[22]  C.G. Cassandras,et al.  Optimal control of hybrid systems in manufacturing , 2000, Proceedings of the IEEE.

[23]  C. Pinello,et al.  Automotive engine control and hybrid systems: challenges and opportunities , 2000, Proceedings of the IEEE.

[24]  Michael D. Lemmon.  On the Existence of Solutions to Controlled Hybrid Automata , 2000, HSCC.

[25]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[26]  Roger W. Brockett,et al.  Hybrid Models for Motion Control Systems , 1993 .

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

[28]  O. Stursberg,et al.  Continuous-discrete interactions in chemical processing plants , 2000, Proceedings of the IEEE.

[29]  J. Lygerosy,et al.  On the Regularization of Zeno Hybrid Automata , 1999 .

[30]  A. T. Fuller,et al.  Relay control systems optimized for various performance criteria , 1960 .

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

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