The multi-disciplinary research field of hybrid systems has emerged over the last decade and lies at the boundary of computer science, control engineering and applied mathematics. In general, a hybrid system can be defined as a system built from atomic discrete components and continuous components by parallel and/or serial composition, arbitrarily nested. The behaviors and interactions of components are governed by models of computation.
Hybrid phenomena captured by such mathematical models are manifested in a great diversity of complex engineering applications such as real-time systems, embedded software, robotics, mechatronics, aeronautics, and process control. The high-profile and safety-critical nature of such applications has fostered a large and growing body of work on formal methods for hybrid systems: mathematical logic, computational models and methods and automated reasoning tools supporting the formal specification and verification of performance requirements for hybrid systems, and the design and synthesis of control programs for hybrid systems that are provably correct with respect to formal specifications.
This course investigates modeling, analysis and verification of various classes of hybrid systems. Special attention is paid to computational and simulation tools for hybrid systems. Applications ranging from networked sensors, power electronics, avionics, autonomous vehicles will be covered. The course consists of lectures, a handful of homework assignments, and a final project.
Office: 514 Cory Hall
Office Hours: Monday Wednesday 3:00pm-4:00pm
Students should understand basic concepts in differential equations, dynamical systems and logic. They should know how to program in some language: for example, Matlab, Mathematica, Java or C. Familiarity with control theory and/or automata theory is useful. Thus a course like EECS 221A or CS 170 is desirable, but not essential.
hscc_ee291e at robotics.eecs.berkeley.edu
Problem Set on Hybrid Systems by John Lygeros
Solution Set to Problem Set on Hybrid Systems by John Lygeros
Potential project topics are maintained by Jonathan Sprinkle
at Projects List
J. Lygeros Lecture Notes on Hybrid Systems, Notes for an ENSIETA short course, Feb 2004.
J. Lygeros, C. Tomlin and S. Sastry Art of Hybrid Systems, Compendium of Lecture Notes for the Hybrid Systems Class, 2002.
P. J. Mosterman An Overview of Hybrid Simulation Phenomena and their support by simulation packages, in HYbrid Systems: COmputation and COntrol, W. VaanDrager and J. van Schuppen (editors), Springer Verlag Lectures Notes in Computer Science, Vol. LNCS-1569, 1999, pp. 178-192.
Luca Carloni, Maria D. Di Benedetto, Alessandro Pinto and Alberto Sangiovanni-Vincentelli Modeling Techniques, Programming Languages Design Toolsets and Interchange Formats for Hybrid Systems EU-IST Columbus Project, DHS3 Report, 2004
G. Lafferiere, G. J. Pappas and S. Sastry O-Minimal Hybrid Systems Mathematics of Control, Signals and Systems, Vol. 13. No. 1, pp. 1-21, March 2000
G. J. Pappas and co-authors Papers on Extensions of Model Checking Methods to Many Interesting Classes of Systems
I. M. Mitchell, A, M. Bayen, C. Tomlin A Time Dependent Hamilton-Jacobi Equation Formulation of Reachable Sets for Continuous Dynamical Systems To appear in the IEEE Transaction in Automatic Control, 2005 (month tbd)
H. de Jong, J.-L. Gouzé, C. Hernandez, M. Page, T. Sari, J. Geiselmann (2003), Hybrid modeling and simulation of genetic regulatory networks: A qualitative approach, Hybrid Systems: Computation and Control, HSCC 2003, Lecture Notes in Computer Science 2623, 267-282.
C. Belta, P. Finin, L.C.G.J.M. Habets, A. Halasz, M. Imielinski, V.Kumar, and H. Rubin, Understanding the bacterial stringent response using reachability analysis of hybrid systems Hybrid Systems: Computation and Control, HSCC 2004, Lecture Notes in Computer Science 2993, 111-126.
Lincoln, P. and Tiwari, A., Symbolic systems biology: Hybrid modeling and analysis of biological networks Hybrid Systems: Computation and Control, HSCC 2004, Lecture Notes in Computer Science 2993, 660-672
Joshi, K. Neogi, N., and W. Sanders, Dynamic Partitioning of Large Discrete Event Biological Systems for Hybrid Simulation and Analysis Hybrid Systems: Computation and Control, HSCC 2004, Lecture Notes in Computer Science 2993
R. Alur, T.A. Henzinger, H. Wong-Toi. Symbolic analysis of hybrid systems. Proceedings of the 37th IEEE Conference on Decision and Control, Invited survey, 1997.
Thomas A. Henzinger, The Symbolic Approach to Hybrid Systems, (CAV '02), UC Berkeley,
E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pnueli, Effective
Synthesis of Switching Controllers for Linear Systems,
In Proceedings of the IEEE, 88, Special Issue Hybrid System: Theory & Applications, 1011-1025, 2000.
Thao Dang, Alexandre Donze, and Oded Maler, Verification of Analog and Mixed-Signal Circuits using Hybrid Systems Techniques, Submitted to DAC'04 - Design Automation Conference, June 2004.
B. H. Krogh and O. Stursberg, On efficient representation and computation of reachable sets for hybrid systems, in Hybrid Systems: Computation and Control (HSCC'03), Lecture Notes in Computer Science (LNCS), Springer..
Paulo Tabuada and George J. Pappas, Linear temporal logic control of linear systems, IEEE Transactions on Automatic Control, Submitted February 2004.
Gerardo Lafferriere, George J. Pappas, and Sergio Yovine, Symbolic reachability computations for families of linear vector fields, Journal of Symbolic Computation, 32(3):231-253, September 2001.
C. Tomlin, I. Mitchell, A. Bayen, and M. Oishi, Computational
Techniques for the Verification and Control of Hybrid
Proceedings of the IEEE, Volume 91, Number 7, July 2003.
Claire Tomlin, John Lygeros, and Shankar Sastry, A Game Theoretic Approach to Controller Design for Hybrid Systems, Proceedings of the IEEE, Volume 88, Number 7, July 2000.
Matthew Senesky, Gabriel Eirea, and T. John Koo, Hybrid Modelling and Control of Power Electronics, Hybrid Systems: Computation and Control April, Lecture Notes in Computer Science, Vol. 2623, pp. 450-465, Springer-Verlag, 2003.
T. J. Koo, S. Sastry, Bisimulation Based Hierarchical System Architecture for Single-Agent Multi-Modal Systems, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, Vol. 2289, pp. 281-293, Springer-Verlag, 2002.
|Examples: Hybrid Automata|
|Modeling: Finite State Machine||Finite state Machines|
|Modeling: Ordinary Differential Equations
|Analysis: Reachability - Discrete||Discete Reachability|
|Analysis: Reachability - Continuous||Continuous Reachability|
|Analysis: Reachability - Hybrid||Hybrid Reachability|
|Analysis: Reachability -
II - Multi-Modal Systems
|Tool: Ptolemy II - Multi-Modal
|March 22||No Class|
|March 24||No Class|
|Computation: Hybrid Automata
|Verification: Temporal Logic|
|Verification: Model Checking|
Application: Sensor Network
|Verification: Timed Automata||Model Checking for Timed Automata|
|Verification: Time Automaton|
|Verification: Time Automaton|
|Verification: Time Automaton|
|Summary: Hybrid Automaa|
Tool: Requiem,d/dt ,Checkmate
|Games and Maximal Invariant Sets||Church and Hamilton Jacobi based Invariant Set Computation|
|Overview of Hybrid Systems with applications||Hybrid Systems: Modeling, Analysis and Control|
|Eckman Award Plenary talk by Professor Claire Tomlin , American Control Conference, July 2004||Hybrid Control: from Air Traffic to Fly Wings||Guest lecture by Professor Alex Bayen ,||Computing Reach Sets Using A Modified Hamilton Jacobi Equation||Guest lecture by Professor Alex Bayen ,||A Viability Theory Approach to Hybrid Systems See also the lecture notes by Lygeros|