Abstract
The connections between two research areas, intelligent control systems and multi-dimensional systems, are established. Two-dimensional (2-D) system theory is used to analyze a class of learning control system. The 2-D state-space model of a learning control system is given. A class of learning control laws is proposed and the convergence of the learning process can be checked based on a 2-D model of the learning control system. The theory and methods proposed in this paper not only provide the learning control system with powerful tools for analysis and design, but also offer a multi-dimensional system theory with a new field of application as well as some new problems for further exploration.
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References
AhmedA., On the stability of two-dimensional discrete systems, IEEE Trans. Automatic Control 25, No. 3, 551 (1980).
ArimotoS., KawamuraS. and MiyazakiF., Bettering operation of robots by learning, J. Robotic Systems 1, No. 2, 123 (1984).
Arimoto, S., Kawamura, S. and Miyazaki, F., Can mechanical robots learn by themselves?, Proc. 2nd Int. Symp. on Robotics Research, Kyoto, Japan (Aug. 1984).
Bose, N.K., Multidimensional System: Theory and Application, IEEE Press (1979).
FuK.S., Learning control systems — Review and outlook, IEEE Trans. Automatic Control AC-15, 210 (1970).
FuK.S., Learning control systems and intelligent control systems: An intersection of artificial intelligence and automatic control, IEEE Trans Automatic Control AC-16, 70 (1971).
Geng, Z. and Carroll, R.L., Eigenstructure assignment of 2-D linear systems, Proc. ISMM Int. Conf. on Computer Applications in Design, Simulation and Analysis, Reno (Feb. 1989).
Geng, Z. and Jamshidi, M., An expert self-learning controller for robot manipulators, Proc. IEEE 27th CDC, Austin, TX (Dec. 1988).
Geng, Z., Jamshindi, M. and Liebowitz, J., Design of self-learning controllers using expert system techniques, Proc. IEEE Int. Symp. on Intelligent Control 1988, Arlington, VA (Aug. 1988).
Geng, Z. and Jamshidi, M., Two-dimensional system models for learning control systems, Proc. Second Int. Symp. on Robotics and Manufacturing, Albuquerque, NM (Nov. 1988).
KungS.Y., LevyB.C., MorfM. and KailathT., New results in 2-D systems theory, Part II: 2-D state-space models-realization and the notions of controllability, observability and minimality, Proc. IEEE 65, No. 6, 945 (1977).
MichalskiR., CarbonellJ. and MitchellT., Machine Learning: An Artificial Intelligence Approach, Vols I, II, Tioga Publishing, Palo Alto (1985).
RoesserR.P., A discrete state-space model for linear image processing, IEEE Trans. Automatic Control AC-20, 1–10 (1975).
SaridisG.N., Application of pattern recognition methods to control systems, IEEE Trans. Automatic Control AC-26, No. 3, 638 (1981).
Simon, H., Why should machine learn? in Machine Learning, Springer-Verlag, p. 25 (1984).
Tsypkin, Y.Z. and Nikolic, Z., Adaptation and Learning in Automatic Systems, Academic Press, Inc. (1971).
Tzafestas, S.G., Multidimensional Systems-Techniques and Applications, Marcel Dekker, Inc. (1986).
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Geng, Z., Jamshidi, M. Learning control system analysis and design based on 2-D system theory. Journal of Intelligent and Robotic Systems 3, 17–26 (1990). https://doi.org/10.1007/BF00368970
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DOI: https://doi.org/10.1007/BF00368970