Abstract
By a “hybrid system” we mean a system of continuous plants, subject to disturbances, interacting with sequential automata in a network. “Hybrid Control” is the name we give to control of continuous plants by digital sequential control automata, that is, by control programs implemented on sequential automata. We associate, without using any approximations, sequential automata with continuous plants, and use this to bring sequential control automata and continuous plants into automata networks which themselves are sequential automata modelling hybrid systems. To be useful, the control automaton's ability to control plant trajectories in a hybrid system should be maintained under small changes in control laws, disturbance, trajectory, measurement, etc. We formalize this notion of controllability and observability for hybrid systems by continuity of system functions, including the input-output function of the control automaton, in non-Hausdorff subtopologies of the usual topologies on spaces of controls, sensor data, plants, disturbances, target sets, etc. These subtopologies arise from the limited ability of digital programs to discriminate between continuous inputs. These notions are appropriate for any knowledge or rule based system where automated deduction interacts in real time with the external world. This topological approach was announced in [46]. (What we call “controllability and observability” here is what we called “stability” in [46] in order to correspond somewhat more closely to usage in the literature [3].)
Research supported by ORA Corp., DARPA-US ARMY AMCCOM (Picatinny Arsenal,NJ) contract DAAA21-92-C-0013, the U. S. Army Research Office contract DAAL03-91-C-0027.
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V. M. Alekseev, V. M. Tikhomirov, S. V. Fomin, Optimal Control, Consultant's Bureau, Plenum Press, 1987.
K.R. Apt and E-R. Olderog, Verification of Sequential and Concurrent Programs, Springer-Verlag, 1991.
M. Arbib and R. E. Kaiman, Topics in Mathematical Systems Theory, McGraw-Hill, N. Y., 1969.
M. Arbib and L. Padulo, Systems Theory, Saunders, Philedelphia, 1974.
J. P. Aubin, Convex Analysis and Optimization, Pitman, 1982.
J. P. Aubin, Differential Inclusions, Set Valued Maps, and Viability, Springer-Verlag, 1984.
J. P. Aubin, Set Valued Analysis, Birkhauser, 1990.
J. P. Aubin, Viability Theory, Birkhauser, 1991.
J. P. Aubin and I. Ekeland, Applied Non-Linear Analysis, Wiley, 1984.
L.D. Berkovitz, Thirty Years of Differential Games, in Modern Optimal Control, Emilio O. Roxin, ed., Marcel Dekker, Inc., 1989.
M. Ben-Ari, Principles of Concurrent Programming, Prentice-Hall, 1990.
R. S. Boyer, M. W. Green, J. S. Moore, The Use of a Formal Simulator to Verify a Simple Real Time Control Program, Technical Report No. ICSA-CMP-29, Institute for Computing Science and Computer Applications, The University of Texas at Austin, SRI International, 1982.
E. Bradley, Control Algorithms for Chaotic Systems, AI Memo 1278, MIT AI Laboratory, 1991.
E. Bradley and F. Zhao, Phase-Space Control System Design, IEEE CACSD92, 1992.
J. R. Büchi, The Collected Works of J. Richard Büchi, S. MacLane, D. Siefkes, eds., Springer-Verlag, 1990.
K. M. Chandy and J. Misra, An Introduction to Parallel Program Design, Addison-Wesley, 1988.
N. Coleman, An Emulation-Simulation for Intelligent Controls, Proc. of the Workshop on Software Tools for Distributed Intelligent Control Systems, 37–52, July 17–19, 1990, Pacifica, California.
R. T. Dodhiawala, V. Jagoenthan, and L. S. Baum, Erasmus System Design: Performance Issues, Proc. of the Workshop on Blackboard Implementation Issues, AIII, Seattle, WA, July, 1987.
Ph. Dwinger and R. Balbes, Distributive Lattices, Columbia, University of Missouri Press, 1974.
S. Eilenberg, Automata, Languages, and Machines (vol. A), Academic Press, New York, 1974.
I. Ekeland, Infinite Dimensional Optimization and Convexity, University of Chicago Lecture Notes in Mathematics, University of Chicago Press, 1983.
A. F. Filippov, Differential Equations with Discontinuous Right Hand Side, Kluwer Academic Publishers, 1988.
A. Friedman, Differential Games, Wiley-Interscience, 1971.
G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott, A Compendium of Continuous Lattices, Springer-Verlag, 1980.
R. L. Grossman and R. G. Larson, Viewing Hybrid Systems as Products of Control Systems and Automata, Proc. IEEE 31st CDC, vol. 3, 2953–2955, Tucson, 1992.
J. Guckenheimer, A. Back, M. Myers, A Dynamical Simulation Facility for Hybrid Systems, this vol.
J. Guckenheimer and A. Nerode, Simulation for Hybrid and Nonlinear Control, Proc. IEEE 31st CDC, vol. 3, 2981–2983, 1992.
Y. Gurevich and L. Harrington, Trees, Automata and Games, Proc. of the 14th Ann. ACM Symp. on Theory of Comp., pp. 60–65, 1982.
O. Hajek, Pursuit Games, Mathematics in Science and Engineering, vol. 120, Academic Press, New York, 1975.
J. Hilgert, K. H. Hofmann, J. Lawson, Lie Groups, Convex Cones, and Semigroups, Oxford Clarendon Press, 1988.
A. Isidori, Nonlinear Control Systems, An Introduction, Springer-Verlag, 1989.
R. Iseman, Digital Control Systems, Springer-Verlag, 1977.
R. Isaacs, Differential Games, SIAM Series in Applied Mathematics, John Wiley and Sons, Inc., 1965.
Y. Kesten and A. Pnueli, Timed and Hybrid Statecharts and their Textual Representation, in Formal Techniques in Real Time and Fault Tolerant Systems, LNCS 571, Springer-Verlag, 1992.
W. Kohn, A Declarative Theory for Rational Controllers, Proc. 27th CDC, pp. 130–136, 1988.
W. Kohn, The Rational Tree Machine: Technical Description and Mathematical Foundations, IR and DBE-499, Technical Document 905-10107-1, July 7, 1989, Boeing Computer Services.
W. Kohn, Rational Algebras: A Constructive Approach, IR and DBE-499, Technical Document D-905-10107-2, July 7, 1989.
W. Kohn, Hierarchical Control Systems for Autonomous Space Robots, Proc. AIAA, 1988.
W. Kohn, Application of Declarative Hierarchical Methodology for the Flight Telerobotic Servicer, Boeing Document G-6630-061, Final Report of NASA-Ames Research Service request 2072, Job Order T1988, Jan 15, 1988.
W. Kohn, Cruise Missile Mission Planning: A Declarative Control Approach, Boeing Computer Services technical Report, 1989.
W. Kohn, Declarative Multiplexed Rational Controllers, Proc. 5th IEEE Int. Symp. Intelligent Cont., pp. 794–803, 1990.
W. Kohn, Declarative Hierarchical Controllers, Proc. Darpa Workshop on Software Tools for Distributed Intelligent Control Systems, Domain Specific Software Initiative, pp. 141–163, Pacifica, Ca., July 17–19, 1990.
W. Kohn, Advanced Architecture and Methods for Knowledge-Based Planning and Declarative Control, Boeing Computer Services Technical Document IRD BCS-021, 1990, in ISMIS 91.
W. Kohn and K. Carlsen, Symbolic Design and Analysis in Control, Proc. 1988 Grainger Lecture Series, U. of Illinois, pp. 40–52, 1989.
W. Kohn and A. Murphy, Multiple Agent Reactive Shop Control, ISMIS91.
W. Kohn and A. Nerode, An Autonomous Control Theory: An Overview, Proc. IEEE CACSD92, March, 1992.
W. Kohn and A. Nerode, Multiple Agent Autonomous Control Systems, Proc. CDC92, Dec, 1992.
W. Kohn and A. Nerode, Multiple Agent Autonomous Control, A Hybrid Systems Architecture, to appear in Logical Methods: A Symposium in honor of Anil Nerodels 60th birthday, Birkhauser, 1993.
W. Kohn and A. Nerode, Multiple Agent Hybrid Control Architecture, this vol.
W. Kohn and T. Skillman, Hierarchical Control Systems for Autonomous Space Robots, Proc. AIAA Conf. on Guidance, Navigation, and Control, v. 1, pp.382–390, 1988.
N.N. Krasovskii and A.I. Subbotin, Game-Theoretical Control Problems, Springer-Verlag, 1988.
W. Kuich and A. Salomaa, Semirings, Automata, Languages, Springer-Verlag, 1985.
B. C. Kuo, Digital Control Systems, Holt, Rinehart, Winston, 1980.
J. W. S. Liu, Real Time Responsiveness in Distributed Operating Systems and Databases, Proc. Darpa Workshop on Software Tools for Intelligent Control, Domain Specific Software Initiative, pp. 185–192, Pacifica, Ca., July 17–19, 1990.
Z. Manna and A. Pnueli, The Temporal Logic of Reactive and Concurrent Systems, Springer-Verlag, 1992.
O. Maler, Z. Manna, and A. Pnueli, Prom Timed to Hybrid Systems, in Proc. Rex Workshop, Real Time in Theory and Practice, J. W. DeBakker, C. Huizing, W. P. de Roever, G. Rozenberg, eds., LNCS 600, Springer Verlag, 1992.
E. Mettala, Domain Specific Architectures, Proc. of Workshop on Domain Specific Software Architectures, 193–231, July 9–12, 1990, Hidden Valley, Calif.
R. McNaughton, Infinite Games Played on Finite Graphs, Tech. Report 92-14, Dept. Comp. Sci., RPI, Troy, New York, May 1992.
M. Mesarovic and Y. Tashahara, Theory of Hierarchical Multilevel Systems, Academic Press, N.Y., 1970.
A. Nerode, General Topology and Partial Recursive Functionals, in Summaries of Talks at the AMS Summer Insitute in Symbolic Logic, Cornell University, 1957.
A. Nerode, Some Stone Spaces and Recursion Theory, Duke Mathematics Journal, 26, 1959, 397–406.
A. Nerode, Modelling Intelligent Control, Proc. DARPA Workshop on Software Tools for Distributed Intelligent Control Systems, Domain Specific Software Initiative, Pacifica, Ca., July 17–19, 1990.
A. Nerode and J.B. Remmel, A Model for Hybrid Systems, Hybrid System Workshop Notes, MSI, Cornell University, Ithaca, NY, June 10–12, 1991.
A. Nerode, J.B. Remmel and A. Yakhnis, Playing Games on Graphs: Extracting Concurrent and Hybrid Control Programs, in prep.
A. Nerode, A. Yakhnis, Modelling Hybrid Systems as Games, Proc. CDC92, pp.2947–2952, Dec, 1992.
A. Nerode, A. Yakhnis, V. Yakhnis, Concurrent Programs as Strategies in Games, in Logic from Computer Science, Y. Moschovakis, ed., Springer-Verlag, 1992.
A. Nerode, A. Yakhnis, V. Yakhnis, Distributed Concurrent Programs as Strategies in Games, to appear in Logical Methods: A Symposium in honor of Anil Nerodels 60th birthday, Birkhauser, 1993.
P. H. Nii, Blackboard Systems: The Blackboard Model of Problem Solving and the Evolution of the Blackboard Architecture, AI Magazine, (7) 2, pp. 38–53, 1986.
L. E. Neustadt, Optimization, Princeton University Press, 1976.
A. Pnueli, Application of Temporal Logic to the Specification and Verification of Reactive Systems: A Survey of Current Trends, in Current Trends in Concurrency, LICS 1986.
A. Pnueli, R. Rosner, On the Synthesis of a Reactive Module, Proc. of 1989 POPL Conference, January 1989.
L.S. Pontryagin, On the Theory of Differential Games, Russian Mathematical Surveys 21 (No.4), pp. 193–246, 1966.
M. H. Raibert, Legged Robots that Balance, MIT Press, 1986.
S. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence, and Robustness, Prentice-Hall, 1989.
M. Schoppers, Automatic Synthesis of Perception Driven Discrete Event Control Laws, Proc. 5th IEEE Inter. Symp. on Intelligent Control, 1990.
M. G. Singh, Dynamical Hierarchical Control, North Holland, Amsterdam, 1977.
T. Skillman, W. Kohn, et. al., Classes of Hierarchical Controllers and their Blackboard Implementations, J. Guidance and Control and Dynamics, (13), pp. 176–182, 1990.
J.J. E. Slotine and Weiping Li, Applied Nonlinear Control, Prentice Hall, 1991.
E. D. Sontag, Mathematical Control Theory, Springer-Verlag, 1990.
H. J. Sussman and V. Jurdjevic, Controllability of Non-linear Systems, J. Diff. Equations, 12 pp.95–116, 1972.
J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, 1972.
J. Warga, Some Selected Problems of Optimal Control, in Modern Optimal Control, Emilio O. Roxin, ed., Marcel Dekker, Inc., 1989.
A. Yakhnis, Game-Theoretic Semantics for Concurrent Programs and their Specifications, Ph. D. Diss., Cornell University, 1990.
A. Yakhnis, Hybrid Games, Technical Report 92-38, Mathematical Sciences Institute, Cornell University, October, 1992.
A. Yakhnis, V. Yakhnis, Extension of Gurevich-Harrington's Restricted Memory Determinacy Theorem, Ann. Pure and App. Logic, 48, 277–297, 1990.
L. C. Young, Optimal Control Theory, Chelsea Pub. Co. N.Y, 1980.
F. Zhao, Extracting and Representing Qualitative Behaviors of Complex Systems in Phase Space, AI Memo 1274, MIT AI Laboratory, March, 1991.
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Nerode, A., Kohn, W. (1993). Models for hybrid systems: Automata, topologies, controllability, observability. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds) Hybrid Systems. HS HS 1992 1991. Lecture Notes in Computer Science, vol 736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57318-6_35
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