Hybrid Systems

Research Projects

• Model-based Integration of Embedded Systems (Mobies)
The Darpa Mobies program sought to develop software technologies for implementing an end-to-end model-based design and implementation approach. Our effort, ``SmartVehicles: An open platform for the design, testing, and implementation of automotive embedded systems,'' led to two test beds, one dealing with engine and powertrain control and the other with vehicle-to-vehicle (V2V) coordinated control. The former was used to develop/test control strategies specific to engine and transmission systems. The V2V test bed developed and tested strategies for collision-warning and adaptive cruise control. The final report is available here:
Final Report [pdf 7.3M]
• Towards a System Design Discipline

System design is a craft and a discipline. Practice of the craft requires domain knowledge. This NSF-sponsored project seeks to formulate a discipline of design through a graduated approach to system description frameworks, behavior, implementation and performance. The approach will build on existing work in hybrid systems, hierarchical and distributed control, and elements of cognitive science and intelligent systems. Some new theoretical and computational material will be developed while filling in gaps and exploring promising directions. The end product of this effort will be: (1) articles and a monograph describing our approach to system design; (2) software tools that aid in the creation of the design, its validation and implementation; and (3) designs that offer solutions to concrete problems in transportation and communication networks. The approach is intended for engineers and students engaged in the design of large, distributed dynamical systems.

Recent Publications

• A comparison principle for equations of the Hamilton-Jacobi type in set-membership filtering.

A.B. Kurzhanski and P. Varaiya. Communications in Information and Systems, Vol 6(3), pp. 179-192, 2006. [pdf 198K]
• Ellipsoidal techniques for reachability analysis of discrete-time linear systems.

A. Kurzhanskiy and P. Varaiya, June 2005. IEEE Trans. Automatic Control, vol 52(1), pp. 26-38, Jan. 2007 [pdf 1.3M]
• Optimization techniques for state-constrained control and obstacle problems.

A.B. Kurzhanski, I.M. Mitchell and P. Varaiya. Journal of Optimization Theory and Applications, vol 128(3), pp. 499-521, March 2006. [pdf 525K]
• Ellipsoidal techniques for hybrid dynamics: the reachability problem.

A. B. Kurzhanski and P. Varaiya, 2005. In W.P. Dayawansa, A. Lindquist, and Y. Zhou (Eds) New Directions and Applications in Control Theory, Lecture Notes in Control and Information Sciences, vol 321, pp.193--205, Springer, 2005. [pdf 421K]
• Reachability under uncertainty and measurement noise.

A.B. Kurzhanski and P. Varaiya, July 2004. To appear in Mathematical Modeling and Simulation. [pdf 172K]
• Ellipsoidal techniques for hybrid dynamics: the reachability problem

A.B. Kurzhanski and P. Varaiya, May 2004. Proc. MTNS, 2005. [pdf 140K]
• Ellipsoidal techniques for reachability under state constraints.

A.B. Kurzhanski and P. Varaiya November 2003. [pdf 272K]
• Reachability under uncertainty.

A.B. Kurzhanski and P. Varaiya, August 2002. Proc 2002 IEEE Conference on Decision and Control. [pdf 284K]
• On ellipsoidal techniques for reachability analysis. Part I. External approximations. Part II. Internal approximations, box-valued constraints.

A.B. Kurzhanski and P. Varaiya, Sept 2000. Optimization: methods and software vol 17, 207-237, 2002.[pdf 298K, 560K] [pdf 886K]
• On reachability under uncertainty,

A.B. Kurzhanski and P. Varaiya. Sept 1999. SIAM J. Control, Vol 41(1), 181--216, 2002. [pdf 268K]
• Dynamic optimization for reachability problems.

A.B. Kurzhanski and P. Varaiya, July 2000. JOTA 108(2), 227--251, 2001. [pdf 886K]
• Control design of an automated highway system,

R. Horowitz and P. Varaiya, Feb. 2000. Proc. of the IEEE 88(7), 913--925, 2000. [pdf 219K]
• Ellipsoidal techniques for reachability analysis. Internal approximation.

A.B. Kurzhanski and P. Varaiya, Sept. 1998. Systems and Control Letters 41, 201--211, 2000.[pdf 279K]
• On the reachability problem under persistent disturbances,
  A.B. Kurzhanski and P. Varaiya, Doklady Mathematics, vol 61(3), 3809-3814, 2000.
• Ellipsoidal techniques for reachability analysis,

A.B. Kurzhanski and P. Varaiya, Dec. 1999. LNCS 1790, 202--214, 2000. [pdf 274K]
• Reach set computation using optimal control,

P. Varaiya, Dec. 1998. [postscript 148K]
• Epsilon approximations of differential inclusions,

A. Puri, P. Varaiya and V. Borkar. Also in Hybrid Systems III, LNCS 1066:362-376, Springer, 1996. [postscript, 513K]
• Driving Safely in Smart Cars,

A. Puri and P. Varaiya. California PATH Research Report UCB-ITS-PRR-95-24. August 1995. Also in Proc. American Control Conference: 3597-3599, 1995. [pdf, 170K]
• What's Decidable About Hybrid Automata ?,

P. Kopke, T. Henzinger, A. Puri and P. Varaiya. 27th Annual ACM Symposioum on Theory of Computing (STOCS): 372-382, 1995. [postscript, 318K]
• The Rabin index and chain automata, with applications to automata and games,

S. Krishnan, A. Puri, R. Brayton and P. Varaiya. Proc. CAV 95. July 1995. [postscript, 221K]
• Verification of Hybrid Systems using Abstractions,

A. Puri and P. Varaiya. Hybrid Systems Workshop, October, 1994. Also Hybrid Systems II, LNCS 999: 359-369, Springer-Verlag, 1995. [postscript, 248K]
• Decidable Hybrid Systems,

A. Puri and P. Varaiya. Computer and Mathematical Modeling,23(11/12):191-202, 1996. [postscript, 359K]
• Stability of Hybrid Systems.

M. Kourjanski and P. Varaiya. 1995. Also in Hybrid Systems III, LNCS 1066:413,423, Springer, 1996.[postscript, 3.2M]
• Viable Control of Hybrid Systems.

A. Deshpande and P. Varaiya. In Hybrid Systems II, LNCS 999:128-147, Springer-Verlag. 1995. [postscript, 356K]
• Information Structures for Control and Verification of Hybrid Systems.

A. Deshpande and P. Varaiya. American Control Conference 1995. [postscript, 151K]
• Decidability of hybrid systems with rectangular differential inclusion,

A. Puri and P. Varaiya. Proc. CAV 94. July 1994. [postscript, 275K]
• Smart cars on smart roads: Problems of control,

P. Varaiya. IEEE Trans. Auto. Control. Vol 38(2), 195-207, Feb. 1993. [pdf, 1.2M]