DISCRETE-TIME FEEDBACK ERROR LEARNING
Keywords:
Discrete-time system, Feedback Error Learning, strictly positive rea, learning controlAbstract
In this study, a theoretical foundation on the Discrete-Time Feedback Error Learning (DTFEL) method is established. This is analogous to the original continuous-time version Feedback Error Learning (FEL) method which is proposed as a control model of cerebellum in the field of computational neuroscience. The FEL is an adaptive control method for two-degree-of-freedom control schemes. In this control scheme the adaptive controller must become an inverse system of the plant. DTFEL is proposed because now the controller is computer-based, which means that the digital control scheme is used instead of the analog one. Many control algorithms are also computed in discrete-time format. Furthermore, some systems are themselves inherently discrete and, certainly for these systems, it is useful to have results available in discrete version for controlling. The ready-to-use controller is the key target of this study.
References
de la Sen, M. (2000). Preserving positive realness through discretization. Proceedings of the American Control Conference; June 28-30, 2000; Chicago, Illinois, p. 1, 144- 1,148.
Gomi, H., and Kawato, M. (1993). Neural network control for a closed-loop system using feedback-error-learning. Neural Net works, 6:933-946.
Jagannathan, S. (1996). Discrete-time adaptive control of feedback linearizable nonlinear systems. IEEE Proceedings of the 35th Conference on Decision and Control; December 11-13, 1996; Kobe, Japan, p. 4,747-4,752.
Kawato, M., Furukawa, K., and Suzuki, R. (1987). A hierarchical neural network model for control and learning of voluntary movement. Biological Cybernetics, 57:169-185.
Kongprawechnon, W., and Kimura, H. (1998). J-lossless factorization and -control for discrete-time systems. International J. Of Control, 70(3):423-446
Miyamura, A. (2000). Theoretical analysis on the feedback error learning method, [Master's thesis]. Department of Complexity Science and Engineering, University of Tokyo, Tokyo, Japan, total number of pages.
Miyamura, A., and Kimura, H. (2002). Stability of feedback error learning scheme. Elsevier, System & Control Letters, 45:303-316.
Narendra, K.S., and Valavani, L.S. (1989). Stable Adaptive Systems. book edition. Prentice Hall, International Editions, Eaglewood Cliffs, New Jersey, USA, total number of pages.
Tao, G., and Ioannou, P.A. (1990). Necessary and sufficient conditions for strictly positive real matrices. IEE Proceedings G: Circuits, Devices and Systems, 137(5): 360-366.
Ushida, S., and Kimura, H. (2002). Adaptive control of nonlinear system with time delay based on the feedback error learning method. Proceedings of the 2002 IEEE International Conference on Industrial Technology; December 11-14, 2002; Bangkok, Thailand, p. 360-366.








