Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

troller has to learn the optimal parameters slowly, using the methods described in Sec. 5.

How new information concerning the unknown plant is to be collected and stored, how it is to be used to detect and classify the environment at any instant of time, and how the controller architecture is to be organized for fast, accurate, and stable response, are the subjects of ongoing research.


ACKNOWLEDGMENT

The research reported here was supported by the Office of Naval Research under Grant N00014-95-1-0844.


REFERENCES

Astrom, K. J., & Wittenmark, B. ( 1990). Computer controlled systems, theory and design. Englewood Cliffs, N J: Prentice-Hall.

Baron, A. R. ( 1992). "Neural net approximation". In Proceedings of the Seventh Yale Workshop on Adaptive and Learning Systems (pp. 68-72).

Hale, J., & Kocak, H. ( 1991). Dynamics and bifurcations. Berlin: Springer-Verlag.

Hornik, K., Stinchcombe, M., & White, H. ( 1989). Multilayer feedforward networks are universal approximators. Neural Networks, 2, 359-366.

Hornik, K. Stinchcombe, M., & White, H. ( 1990). Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks, 3, 551-560.

Isidori, A. ( 1989). Nonlinear control systems. Berlin: Springer-Verlag.

Kailath, T. ( 1980). Linear systems, Englewood Cliffs, N J: Prentice-Hall.

Leontaritis, I. J., & Billings, S. A. ( 1985). "Input-output parametric models for nonlinear systems. Part I: Deterministic nonlinear systems". International Journal of Control, 41( 2), 303-328.

Levin, A. U., & Narendra, K. S. ( 1992). "Control of nonlinear dynamical systems using neural networks: Controllability and stabilization". IEEE Transactions on Neural Networks, 4( 2), 192-206.

Levin, A. U., & Narendra K. S. ( 1996, Jan.). "Control of nonlinear dynamical systems using neural networks. Part II: Observability, identification and control". IEEE Transactions on Neural Networks.

Mukhopadhyay, S., & Narendra, K. S. ( 1993). "Disturbance rejection in nonlinear systems using neural networks". IEEE Transactions on Neural Networks, 4( 1), 63-72.

Narendra, K. S. ( 1992). "Adaptive control of dynamical systems using neural networks". In D. A. White and D. Sofge (Eds.). Handbook of intelligent control: neural, adaptive and fuzzy approaches. Von Nostrand, 1992.

Narendra, K. S., & Annaswamy, A. M. ( 1989). Stable Adaptive Systems, Englewood Cliffs, NJ: Prentice-Hall.

Narendra, K. S., & Balakrishnan, J. ( 1992, May). "Performance improvement in adaptive control systems using multiple models and switching". In Proceedings of the Seventh Yale Workshop on Adaptive and Learning Systems (pp. 27-33).

Narendra, K. S., & Balakrishnan, J. ( 1992, October). "Improving transient response of adaptive control systems using multiple models and switching". Tech. Rep. 9212, Yale University, Center for Systems Science, Department of Electrical Engineering, New Haven, CT.

Narendra, K. S., & Cabrera, J. B. D. ( 1994). "Input-output representation and control of discrete-time dynamical systems-Nonlinear ARMA models". In Proceedings of the 33rd IEEE Conference on Decision and Control (pp. 1118-1119).

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