545 Malott Hall
Ph.D. (1956) University of Chicago
Mathematical logic, computability theory, computer science, mathematics of AI, control engineering, quantum control of macroscopic systems
My principal research at present is in theorems and algorithms for extracting controls for hybrid systems using Finsler differential geometry and logic-based controllers. Tools include the relaxed calculus of variations, connections on Finsler manifolds, Lie semigroups, chattering control, and automata theory. I also continue to work on problems in pure and applied logic, including computable model theory of nonstandard logics, automatic structures, foundations of logic programming, and automata models for multiple agent systems.
I am currently working with my long-term co-author in hybrid optimal control, Wolf Kohn, developing quantum hybrid control. The first intended application is to very efficient artificial photosynthesis on silicon, enabled by quantum feedback control.
My professional activities include:
- Chair of the program committee of IEEE-MASS-2005 Security and Survivability Symposium.
- An hour address at IEEE MAS&S2005.
- Keynote speaker at the Tennenbaum Symposium, CUNY, April 2006.
- Chair of the international advisory board of Clearsight Corporation, Bellevue, Washington.
- Member of the international advisory board of Computer Science, NTT, Japan.
- Member of the international advisory board of the Centre for Discrete Mathematics and Theoretical Computer Science, University of Auckland, New Zealand.
- Chair of the steering committee of the Logical Foundations of Computer Science Symposium, scheduled for June 4-7, 2007 at City University, New York City, NY.
- Co-chair of the organizing committee for the IFAC Symposium “Hybrid Systems and Intelligent Control,” scheduled for summer 2007 in Irkutsk, Russia.
Logic, Categories, Lambda Calculus (with R. Platek, G. Odifreddi), in preparation, 500 pp.
Finsler Control Theory and its applications (with W. Kohn, V. Brayman), in preparation, 300 pp.
Tableaux for constructive concurrent dynamic logic (with D. Wijesekera), Annals of Pure and Applied Logic 135 (2005), 1–72.
Effective completeness theorems for modal logic (with S. Ganguli), Annals of Pure and Applied Logic 128 no. 1-3 (2004), 141–195.
Control synthesis in hybrid systems with Finsler dynamics (with Wolf Kohn and Vladimir Brayman), Houston Journal of Mathematics 28 no. 2 (2003), 353–375.
Control in hybrid systems (with W. Kohn, V. Brayman, and P. Cholewinski), Int. J. Hybrid Systems 3 (2003).
Automata Theory and Its Applications (with Bakhadyr Khoussainov), Birkhauser, 2001, 430 pp.
I am also an editor of journals in these fields.