AA278A: Hybrid Systems: Modeling, Analysis, and Control
Stanford University
Spring Quarter 2004-2005

Lecture Information: Gates B12, TTh 11:00 - 12:15.
Section Information: Gates B12, M 12:45-2:05.

Instructor Course Assistant Administrative Associate
Course Description

The revolution in digital technology has fueled a need for design techniques that can guarantee safety and performance specifications of embedded systems, or systems that couple discrete logic with the analog physical environment.

Hybrid systems are dynamical systems with interacting continuous-time dynamics (modeled by differential equations) and discrete-event dynamics (modeled by automata). They are important in applications in CAD, real-time software, robotics and automation, mechatronics, aeronautics, air and ground transportation systems, process control, and have recently been at the center of intense research activity in the control theory, computer-aided verification, and artificial intelligence communities. In the past several years, methodologies have been developed to model hybrid systems, to analyze their behavior, and to synthesize controllers that guarantee closed-loop safety and performance specifications. These advances have been complemented by computational tools for the automatic verification and simulation of hybrid systems.
This course will present the recent advances in modeling, analysis, control, and verification of hybrid systems. Topics will include:

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    E205, E209A, EE263
    MATLAB will be used


    Homework 40%
    Final project 60%

    Textbook and References

    The course is based on a set of lecture notes and articles which will be made available throughout the term. A reading list of relevant articles follows:

    Hybrid Modeling - Reachability Analysis

    1. M. Oishi, I. Mitchell, A. Bayen, C. Tomlin, and A. Degani, Hybrid Verification of an Interface for an Automatic Landing, In the Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, December 2002.
    2. Ian M. Mitchell, Alexandre M. Bayen, and Claire J. Tomlin, A Time-Dependent Hamilton-Jacobi Formulation of Reachable Sets for Continuous Dynamic Games, To appear in the IEEE Transactions on Automatic Control, June 2005.
    3. 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, pp. 986-1001, July 2003.
    4. A Game Theoretic Approach to Controller Design for Hybrid Systems
      Claire Tomlin, John Lygeros, and Shankar Sastry.
      Proceedings of the IEEE, Volume 88, Number 7, July 2000.
    5. Validating a Hamilton-Jacobi Approximation to Hybrid System Reachable Sets
      Ian Mitchell, Alexandre Bayen, and Claire Tomlin
      ©Springer-Verlag 2001, may not be further reproduced without their permission, and is published in Volume 2034 of the LNCS series.
    Hybrid Modeling - Biological Systems
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. R. Ghosh and C. J. Tomlin, Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modeling: Delta-Notch protein signaling, IEE Transactions on Systems Biology, Volume 1, Number 1, pp. 170-183, June 2004.
    Hybrid System Stability
    1. Raymond A. DeCarlo, Michael S. Branicky, Stefan Pettersson, Bengt Lennartson, Perspectives and Results on the Stability and Stabilizability of Hybrid Systems , Proceedings of IEEE, Special Issue on Hybrid Systems, July 2000.
    Hybrid & Optimal Control
    1. Ian Mitchell and C. J. Tomlin, Overapproximating Reachable Sets by Hamilton-Jacobi Projections, Journal of Scientific Computation, Volume 19, Number 1, pp. 323-346, December 2003.
    2. T. Mehta and M. Egerstedt. Learning Multi-Modal Control Programs. To appear in Hybrid Systems: Computation and Control, Springer-Verlag, Zurich, Switzerland, March 2005
    3. Y. Wardi, M. Egerstedt, M. Boccadoro, and E. Verriest. Control of Switching Surfaces. IEEE Conference on Decision and Control, Atlantis, Bahamas, Dec. 2004.
    4. Rantzer, Anders, Approximate dynamic programming in switching systems, IEE Proceedings special issue on Hybrid Systems, Invited paper, to appear in 2005.
    Mixed Integer Linear Programming
    1. Cook, Cunningham, Pulleybank, and Schrijver, Combinatorial Optimization, Wiley 1997.
    2. Robert Fourer, David M. Gay, Brian W. Kernighan, AMPL: A modeling language for mathematical programming, Brooks Cole, 2003
    3. CPLEX Manuals available at /usr/pubsw/doc/Sweet/ilog.