AA278A: Hybrid Systems: Modeling, Analysis, and Control
Spring Quarter 2004-2005
Lecture Information: Gates B12, TTh 11:00 - 12:15.
Section Information: Gates B12, M 12:45-2:05.
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:
continuous-time and discrete-event models
safety specifications and model checking
optimal control theory and differential games
Lyapunov stability analysis and verification tools
a range of engineering examples
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E205, E209A, EE263
MATLAB will be used
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
Hybrid Modeling - Biological Systems
- 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.
- 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.
C. Tomlin, I. Mitchell, A. Bayen, and M. Oishi,
for the Verification and Control of Hybrid Systems,
Proceedings of the IEEE, Volume 91, Number 7, pp. 986-1001, July 2003.
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.
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
2034 of the LNCS series.
Hybrid System Stability
- 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. 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 & Optimal Control
- Raymond A. DeCarlo, Michael S. Branicky, Stefan Pettersson, Bengt Lennartson,
Results on the Stability and Stabilizability of Hybrid Systems , Proceedings
of IEEE, Special Issue on Hybrid Systems, July 2000.
Mixed Integer Linear Programming
- 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.
- T. Mehta and M. Egerstedt.
Learning Multi-Modal Control Programs.
To appear in Hybrid Systems: Computation and Control, Springer-Verlag,
Zurich, Switzerland, March 2005
- Y. Wardi, M. Egerstedt, M. Boccadoro, and E. Verriest.
Control of Switching Surfaces.
IEEE Conference on Decision and Control, Atlantis, Bahamas, Dec. 2004.
- Rantzer, Anders, Approximate dynamic programming in switching systems,
IEE Proceedings special issue on Hybrid Systems, Invited paper, to appear in 2005.
- Cook, Cunningham, Pulleybank, and Schrijver, Combinatorial Optimization, Wiley 1997.
- Robert Fourer, David M. Gay, Brian W. Kernighan, AMPL: A modeling language for mathematical programming, Brooks Cole, 2003
- CPLEX Manuals available at /usr/pubsw/doc/Sweet/ilog.