On consistent symbolic representations of general dynamic systems

This paper deals with the issue of consistent symbolic (qualitative) representation of continuous dynamic systems. Consistency means here that the results of reasoning with the qualitative representation hold in the underlying (quantitative) dynamic system. In the formalization proposed in this paper, the quantitative structure is represented using the notion of a general dynamic system (GDS). The qualitative counterpart (QDS), is represented by a finite-state automaton structure. The two representational substructures are related through functions, called qualitative abstractions of dynamic systems. Qualitative abstractions associate inputs, states and outputs of the QDS, with partitions of appropriate GDS spaces. The paper shows how to establish such consistent partitions, given a partitioning of the system's output. To represent borders of these partitions, the notion of critical hypersurfaces is introduced. One of the main ideas that provides consistency is the interpretation of qualitative input events as elements of the partition of the Cartesian product of input, initial state and time sets. An example of a consistent qualitative/quantitative representation of a simple dynamic system, and of reasoning using such a representation, is provided. >

[1]  P. Krishnaprasad.  System theory: A unified state-space approach to continuous and discrete-time systems , 1978 .

[2]  Michael R. Genesereth,et al.  Logical foundations of artificial intelligence , 1987 .

[3]  G. N. Saridis,et al.  Intelligent robotic control , 1983 .

[4]  A. Meystel.  Nested hierarchical control , 1993 .

[5]  A. Nerode,et al.  Multiple agent autonomous hybrid control systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[6]  Panos J. Antsaklis,et al.  Towards intelligent autonomous control systems: Architecture and fundamental issues , 1989, J. Intell. Robotic Syst..

[7]  Bernard P. Zeigler,et al.  A multimodel methodology for qualitative model engineering , 1992, TOMC.

[8]  Leon S. Levy.  Discrete structures of computer science , 1980 .

[9]  Paul A. Fishwick,et al.  The role of process abstraction in simulation , 1988, IEEE Trans. Syst. Man Cybern..

[10]  P. Struss.  Problems of interval-based qualitative reasoning , 1989 .

[11]  Elisha Sacks,et al.  Automatic Analysis of One-Parameter Planar Ordinary Differential Equations by Intelligent Numeric Simulation , 1991, Artif. Intell..

[12]  George J. Klir,et al.  Architecture of Systems Problem Solving , 1985, Springer US.

[13]  J. Brown,et al.  A Qualitative Physics Based on Confluences , 1984, Artif. Intell..

[14]  Bernard P. Zeigler,et al.  Qualitative physics: towards the automation of systems problem solving , 1991, J. Exp. Theor. Artif. Intell..

[15]  Kenneth Man-kam Yip,et al.  Extracting Qualitative Dynamics from Numerical Experiments , 1987, AAAI.

[16]  Benjamin Kuipers,et al.  Bridging the Gap from Qualitative to Numerical Simulation , 1991 .

[17]  Heidi Therese Dangelmaier.  A qualitative representation for manipulator kinematics and other vector and scalar fields , 1989 .

[18]  Kelvin Lancaster,et al.  The Scope of Qualitative Economics , 1962 .

[19]  Benjamin Kuipers,et al.  Qualitative Simulation , 1986, Artificial Intelligence.

[20]  W. M. Gorman.  More Scope for Qualitative Economics , 1964 .

[21]  Mihajlo D. Mesarovic,et al.  Abstract Systems Theory , 1989 .

[22]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[23]  James Quirk,et al.  Qualitative Problems in Matrix Theory , 1969 .

[24]  P.J. Antsaklis,et al.  Learning to Coordinate Control Policies of Hybrid Systems , 1993, 1993 American Control Conference.

[25]  Herbert Praehofer,et al.  SYSTEM THEORETIC FORMALISMS FOR COMBINED DISCRETE-CONTINUOUS SYSTEM SIMULATION , 1991 .

[26]  Elisha Sacks,et al.  PROLEGOMENA TO ANY FUTURE QUALITATIVE PHYSICS , 1992, Comput. Intell..

[27]  Benjamin J. Kaipers,et al.  Qualitative Simulation , 1989, Artif. Intell..

[28]  Mieczyslaw M. Kokar.  Critical Hypersurfaces and the Quantity Space , 1987, AAAI.

[29]  A FishwickPaul.  An integrated approach to system modeling using a synthesis of artificial intelligence, software engineering and simulation methodologies , 1992 .

[30]  James S. Albus,et al.  Outline for a theory of intelligence , 1991, IEEE Trans. Syst. Man Cybern..

[31]  Qingsu Wang,et al.  TIME WINDOWS: AUTOMATED ABSTRACTION OF CONTINUOUS-TIME MODELS INTO DISCRETE-EVENT MODELS IN HIGH AUTONOMY SYSTEMS∗ , 1991 .

[32]  Bernard P. Zeigler,et al.  Abstracting event-based control models for high autonomy systems , 1993, IEEE Trans. Syst. Man Cybern..

[33]  Fausto Giunchiglia,et al.  A Theory of Abstraction , 1992, Artif. Intell..

[34]  Johan de Kleer,et al.  Readings in qualitative reasoning about physical systems , 1990 .

[35]  Feng Zhao,et al.  Extracting and Representing Qualitative Behaviors of Complex Systems in Phase Spaces , 1991, IJCAI.

[36]  P. Le Guernic,et al.  Hybrid dynamical systems theory and the Signal language , 1990 .

[37]  P. Varaiya,et al.  Hybrid dynamical systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.