Tu-Th 2 -3:30 pm.

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

Email: sastry@eecs.berkeley.edu

URL: http://robotics.eecs.berkeley.edu/~sastry

Homework | 30% |

Project | 70% |

**Prerequisites**

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

March 18th Preliminary Proposal Outline Due

May 9th, 10th Final Project Presentations

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
Systems,*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.*

Date |
Possible Topic(s) |
Downloads |

January 18 | Introduction | Introduction |

Examples: Hybrid Automata | ||

Modeling: Finite State Machine | Finite state Machines | |

Modeling: Timed
Automata Tool: HyTech |
||

Modeling: Ordinary Differential Equations Tool: Matlab |
ODEs | |

Modeling: Hybrid
Automata Tool: HyVisual |
||

Analysis: Reachability - Discrete | Discete Reachability | |

Analysis: Reachability - Continuous | Continuous Reachability | |

Analysis: Reachability - Hybrid | Hybrid Reachability | |

Analysis: Reachability -
Hybrid Tool: Requiem |
||

Tool: Ptolemy
II - Multi-Modal Systems |
||

Tool: Ptolemy II - Multi-Modal
Systems |
||

Presentation: Paper | ||

Presentation: Paper | ||

March 22 | No Class | |

March 24 | No Class | |

Computation: Hybrid Automata Tool: d/dt |
||

Discussion: Projects | ||

Verification: Temporal Logic | ||

Verification: Model Checking | ||

Discussion: Projects | ||

Verification: Time
Automaton Application: Sensor Network |
||

Verification: Timed Automata | Model Checking for Timed Automata | |

Verification: Time Automaton | ||

Verification: Time Automaton | ||

Verification: Time Automaton | ||

Summary: Hybrid Automaa | ||

Computation: Linear
Systems Tool: Requiem,d/dt ,Checkmate |
||

Computation: HSIF | ||

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 |

- Hybrid Systems Course offered at
- University of California at Berkeley
- Vanderbilt University by T. John Koo
- Stanford University by Claire J. Tomin
- University of Pennsylvania by Rajeev Alur and George Pappas

- Online Communities (these sites have lots of further links to Hybrid
Systems topics)
- Virtual Action Group on Hybrid Dynamic Systems for the IEEE's Control Systems Society technical committee on Computer Aided Control System Design.
- IEEE CSS Technical Committee on Hybrid Systems

- Research Groups
- Center for Hybrid and Embedded Systems at Berkeley
- Hybrid Systems Group at the University of Pennsylvania
- Control and Optimization of Hybrid and Embedded Systems Group at the University of Siena
- Hybrid Systems Laboratory at Stanford

- Tools
- CheckMate for verifying hybrid systems.
- Requiem for verifying hybrid systems.
- d/dt for verifying and synthesis hybrid systems.
- HyTech for verifying linear hybrid systems.
- Ptolemy II for simulating concurrent, embedded and hybrid systems.

- Conferences and Workshops
- Hybrid Systems: Computation and Control 2005 in Zurich.
- Hybrid Systems: Computation and Control 2004 in Philadelphia.
- Hybrid Systems: Computation and Control 2003 in Prague.
- IFAC Conference on Analysis and Design of Hybrid Systems in Lyons.
- IEEE Conference on Decision and Control 2004 in Nassau.
- IEEE Conference on Decision and Control 2003 in Maui.