Modeling

Maurice Heemels,

Linear Complementarity Systems: A Study in Hybrid Dynamics, Ph.D. Thesis, Eindhoven University of Technology, Netherlands, 1999. Examples of so-called "complementarity systems" are mechanical systems subject to inequality constraints and consequently, impact phenomena. The characterizing ingredients of complementarity systems are differential equations in conjunction with complementarity conditions (like ideal diode characteristics) consisting of inequalities and Boolean expressions. The complementarity conditions are imposed on a pair of variables (u,y) in the sense that u is nonnegative, y is nonnegative and {u=0 or y=0}.    

Georgina Fábián,

A Language and Simulator for Hybrid Systems, Ph.D. Thesis, Eindhoven University of Technology, Netherlands, 1999. The hybrid Chi language semantics is specified. A hybrid model simulator is developed that integrates a nonlinear equation solver for the initial state and a DAE solver for continuous behavior. Composition of continuous models uses channels that have the semantics of algebraic equations. Combined with the use of local process variables this contributes significantly to clear and robust models.    

Krister Edström,

Switched Bond Graphs: Simulation and Analysis, Ph.D. Thesis, Linköping University, Sweden, 1999. Algorithms for causality propagation, equation generation, and simulation are derived. An efficient algorithm is presented, that detects causality problems like algebraic loops, and derivative and conflicting causality. It is shown that a class of classical bond graphs can be expressed in state space form, by a variable transformation, and that correct initial values of the continuous state variables are achieved when a new mode is entered.  

Emanuele Carpanzano,

A Development Methodology for Hybrid Control Systems, Ph.D. Thesis, Politecnico di Milano, 1998.  

Pieter J. Mosterman,

Hybrid Dynamic Systems: A hybrid bond graph modeling paradigm and its application in diagnosis, Ph.D. Thesis, Vanderbilt University, 1997. This thesis develops a formal hybrid modeling theory based on physical principles, a model verification method, and a physically correct behavior generation algorithm. A postscript version is available.  

M. Otter, C. Schlegel, and H. Elmqvist,

"Modeling and Realtime simulation of an Automatic Gearbox using Modelica", in Proceedings of ESS'97, pp. 115-121, October 19-22, Passau, Germany, 1997. The automatic gearbox consists of 6 switching elements (clutches and freewheels) leading to 64 possible configurations. It is shown how a consistent configuration can be found in realtime after a gearshift occurred (i.e., event iteration is adapted for realtime applications). A postscript version is available.  

Friedrich Pfeiffer and Christoph Glocker,

Multibody Dynamics with Unilateral Contacts, John Wiley and Sons, Inc., 1996. This book contains new research results of the modeling of mechanical systems with friction and impact. The basic approach consists of transforming the problem into a complementary problem that is solved by standard algorithms. Several applications are discussed.

C. Majer, W. Marquardt, and E.D. Gilles,

"Reinitialization of DAEs after Discontinuities", Computers and Chemical Engineering, vol. 19, suppl. S507-S512, 1995. Discusses the re-initialization of DAEs with discontinuities by solving nonlinear consistency equations.

M. Andersson,

Object-Oriented Modelling and Simulation of Hybrid Systems, Ph.D thesis, Lund Institute of Technology, ISRN UTFD2/TFRT--1043--SE, 1994. Object-oriented models of physical systems are transformed into a system of DAEs. A special discrete operator allows the Grafcet method to model the discrete behavior. Event detection and root-finding are discussed.

H. Elmqvist, F.E. Cellier, and M. Otter,

"Object-Oriented Modelling of Power-Electronic Circuits Using Dymola", in Proceedings of CISS'94, pp. 156-161, August 22-25, Zürich, Switzerland, 1994. Describes how to model and simulate power-electronic circuits with many ideal switches. Shows that a simulation speed-up of 20 can be obtained with regards to conventional methods. A postscript version is available.  

H. Elmqvist, F.E. Cellier, and M. Otter,

"Object-Oriented Modelling of Hybrid Systems", in Proceedings of ESS'93, pp. xxxi-xli, October 25-28, Delft, Netherlands, 1993. Introduces higher level elements to describe discrete components. Uses BLT partitioning to order these elements in order that the component equations are evaluated in the correct order at event instants. Introduces event iteration as an alternative to the transformation of a complementary problem. Method is demonstrated at a system with coupled friction elements. A postscript version is available.  

P.I. Barton,

The Modelling and Simulation of Combined Discrete/Continuous Processes, Ph.D. Thesis, University of London, 1992. In this thesis hybrid process engineering systems are modeled by DAEs for the continuous part and by sets of finite automatas for the discrete part of physical models. A postscript version is available.  

H.B. Armstrong,

Control of Machines with Friction, Kluwer Academic Publishers, 1991. One of the rare books about friction modeling for dynamic system analysis and design.

P. Lötstedt,

"Coulomb Friction in Two-Dimensional Rigid Body Systems", Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), vol. 61, pp. 605-615, 1981. This is a classical paper about hybrid mechanical systems. It shows that even for simple mechanical systems the problem specification may lead to a model with no (unique) solution.

Simulation

P.I. Barton and T. Park,

"State Event Location in Differential-Algebraic Models", ACM Transactions on Modelling and Computer Simulation, vol. 6, no. 2, pp. 137-165, 1996. New results on state event location of DAE solvers. A postscript version is available.

E. Eich,

Projizierende Mehrschrittverfahren zur numerischen Lösung von Bewegungsgleichungen technischer Mehrkörpersysteme mit Zwangsbedingungen und Unstetigkeiten, Dissertation, VDI-Fortschritt-Berichte, Reihe 18, Nr. 109, VDI-Verlag, Düsseldorf, 1992. Simulation of hybrid DAEs with projection methods.

François E. Cellier,

Combined Continuous/Discrete System Simulation by Use of Digital Computers: Techniques and Tools, Ph.D. Thesis, Swiss Federal Institute of Technology, ETH Zürich, Switzerland, 1979.

Verification

Mayank B. Amin,

Stabilization and SubOptimal Wavelets Control of Hybrid Dynamical Systems, Ph.D. Dissertation, University of Minnesota, 1999.

Stefan Pettersson,

Analysis and Design of Hybrid Systems, Ph.D. Dissertation, Chalmers University of Technology, June, 1999. It is shown that hybrid systems can be constructed by modular decompositions and hybrid system stability results are presented that are extensions of Lyapunov theory applying an abstract energy function satisfying certain properties. The search for such functions can be formulated as linear matrix inequality (LMI) problems, amenable to computerized methods. It also addresses stability robustness (i.e., stability despite the presence of model uncertainties) and how to switch between different continuous vector fields guaranteeing stability of the closed-loop system.  

Gerardo Lafferriere, George J. Pappas, and Sergio Yovine

"Decidable Hybrid Systems", in KIT Workshop on Verification of Hybrid Systems , October 19-21, Grenoble, France, 1998. This paper extends the decidability frontier for classes of linear hybrid systems, those with linear vector fields in each discrete location. It shows that such hybrid systems admit a finite bisimulation, and presents an algorithm that computes it using decision methods from mathematical logic.

R. Alur and D. Dill,

"A theory of timed automata", Theoretical Computer Science, 126, pp. 183-235, 1994. In this paper timed automata are introduced.

T.A. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine,

"Symbolic model checking for real-time systems", Information and Computation, 111, pp. 193-244, 1994. In this paper, a (branching) real-time temporal logic is introduced.

R. Alur, T.A. Henzinger, and P.-H. Ho,

"Automatic symbolic verification of embedded systems". A preliminary version of the paper appeared in Proceedings RTSS '93, pp. 2-11, IEEE Computer Society Press, 1993. In this paper the model of timed automata is generalized to linear hybrid automata.

Vineet Gupta, Radha Jagadeesan, Vijay A. Saraswat,

"Hybrid CC, Hybrid Automata and Program Verification", Proceedings of Hybrid Systems III, edited by Alur, Henzinger and Sontag, LNCS 1066, Springer Verlag. Demonstrates the relationship of Hybrid CC to the methodology and tools developed in the research on verification of hybrid systems. A postscript version is available.

Rajeev Alur, Costas Courcoubetis, Thomas A. Henzinger, Nicolas Halbwachs, Pei-Hsin Ho, Xavier Nicollin, Alfredo Olivero, Joseph Sifakis, and Sergio Yovine,

"The Algorithmic Analysis of Hybrid Systems", Theoretical Computer Science, to appear. Presents a general framework for the formal specification and algorithmic analysis of linear hybrid systems. Hybrid systems are modeled as finite automata equipped with variables that evolve continuously with time. A postscript version is available.

Specification

P.J.L. Cuijpers and M.A. Reniers,

Hybrid process algebra, Computer Science Report, Eindhoven University of Technology, 2003. A pdf version is available.  

Jennifer M. Davoren,

Modal Logics for Continuous Dynamics, Ph.D. Thesis, Department of Mathematics, Cornell University, 1998. This work is a formal investigation of a number of bimodal and polymodal logics built on a base of propositional S4, and is a contribution to the theory of hybrid control systems. A postscript version is available.  

Moshe Gotesman,

Modeling of Hybrid Dynamic Systems, Ph.D. Thesis, Texas Tech University, 1996. Presents a technique for converting a mathematical or block diagram representation of a hybrid dynamic system into a Hybrid Dynamics Petri Net (HDPN) and vice versa. It also demonstrates the modeling power of Petri nets for nonlinear and MIMO systems.  

VV. Friesen,

"An Exercise in Hybrid System Specification Using an Extension of Z", in Second European Workshop on Real-Time and Hybrid Systems, A. Bouajjani and O. Maler, editors,  pp. 311-316, 1995.Illustrates the main concepts of ZimOO, an extended subset of Object-Z to describe continuous and discrete features by a common formalism. A postscript version is available.

Vineet Gupta, Radha Jagadeesan, Vijay A. Saraswat, Danny G. Bobrow,

"Programming in Hybrid Constraint Languages", Hybrid Systems II, LNCS 999, Springer Verlag, 1994. Presents a declarative language for modeling hybrid systems compositionally. Programs are understood as logical formulas that place constraints upon the temporal evolution of a system. A postscript version is available.