Ludzie pragną czasami się rozstawać, żeby móc tęsknić, czekać i cieszyć się z powrotem.
2001.
overview optimal control theory, especially DP, the LQR, and
[25] R. E. Bellman and S. E. Dreyfus, Applied Dynamic Programming.
Princeton, NJ: Princeton Univ. Press, 1962.
FOC. We point out the problematic aspects as well as the perfor-
[26] R. E. Bellman and R. E. Kalaba, Dynamic Programming and Modern mance benefits of each individual method. In particular, DP pro-Control Theory.
New York: Academic, 1965.
duces the optimal solution that is able to reject disturbances and
[27] D. G. Luenberger, Introduction to Dynamic Systems: Theory, Models, & Applications.
New York: Wiley, 1979.
uncertainties as a result of feedback. However, computation and
[28] G. R. Bolt, “Fault tolerance in artificial neural networks,” Ph.D. disser-storage requirement associated with DP solutions can be prob-
tation, York University, York, ON, Canada, 1992.
lematic, especially for high-order nonlinear systems. Thus, in
[29] D. Rumelhart and J. McClell, Eds., Parallel Distributed Processing: Explorations in the Microstructure of Cognition.
Cambridge, MA: MIT
the companion papers [23], [24], we propose NDO as an approx-Press, 1986, vol. 1.
imate technique for solving the DP problem based on neural network techniques that provides many of the performance benefits (e.g., optimality and feedback) of DP and benefits from the numerical properties of neural networks. Reference [23] presents Chang-Yun Seong (M’01) received the B.S. and
the theory of NDO, and [24] demonstrates the method on sev-M.S. degrees in aerospace engineering from Seoul
eral applications including control of autonomous vehicles and National University, Seoul, Korea, in 1990 and
1992, respectively, and the M.S. degree in electrical
of a robot arm, respectively.
engineering and the Ph.D. degree in aeronautics and
astronautics from Stanford University, Stanford, CA,
R
in 1998 and 2000, respectively.
EFERENCES
He was a Research Engineer with the Systems
[1] G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Engineering
Research
Institute
(SERI/KIST),
Dynamic Systems, Third ed.
Reading, MA: Addison-Wesley, 1994.
Taejon, Korea, before he pursued his graduate
[2] G. F. Franklin, J. D. Powell, and M. L. Workman, Digital Control of studies at Stanford University. He is currently a
Dynamic Systems, Third ed.
Reading, MA: Addison-Wesley, 1998.
Research Engineer with Fineground Networks, Campbell, CA. His research
[3] S.
P.
Boyd,
Linear
Controller
Design:
Limits
of
Perfor-
interests include neural networks, optimization, control systems, and digital mance.
Englewood Cliffs, NJ: Prentice-Hall, 1991.
signal processing.
[4] T. Kailath, Linear Systems.
Englewood Cliffs, NJ: Prentice-Hall, 1980.
Dr. Seong is a member of AIAA. He was a recipient of the Outstanding
[5] J. E. Slotine and W. Li, Applied Nonlinear Control.
Englewood Cliffs,
Teaching Assistant Award from the AIAA Stanford Chapter in 1997.
NJ: Prentice-Hall, 1991.
[6] A. Isidori, Nonlinear Control Systems: An Introduction.
New York:
Springer-Verlag, 1989.
[7] H. K. Khalil, Nonlinear Systems.
New York: Macmillan, 1992.
[8] A. E. Bryson, Dynamic Optimization.
Menlo Park, CA: Ad-
Bernard Widrow (M’58–SM’75–F’76–LF’95) re-
dison-Wesley-Longman, 1999.
ceived the S.B., S.M., and Sc.D. degrees in electrical
[9] F. L. Lewis, Optimal Control, 2nd ed.
New York: Wiley, 1995.
engineering from the Massachusetts Institute of
[10] R. F. Stengel, Optimal Control and Estimation.
New York: Dover,
Technology (MIT), Cambridge, in 1951, 1953, and
1994.
1956, respectively.
[11] R. E. Bellman, Dynamic Programming.
Princeton, NJ: Princeton Univ.
He joined the MIT faculty and taught there from
Press, 1957.
1956 to 1959. In 1959, he joined the faculty of Stan-
[12] S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd ford University, Stanford, CA, where he is currently
ed.
Englewood Cliffs, NJ: Prentice-Hall, 1999.
Professor of Electrical Engineering. He is Associate
[13] B. Widrow and M. A. Lehr, “30 years of adaptive neural networks: Editor of several journals and is the author of about
Perceptron, Madaline, and backpropagation,” Proc. IEEE, vol. 78, pp.
100 technical papers and 15 patents. He is coauthor
1415–42, Sept. 1990.
of Adaptive Signal Processing (Englewood Cliffs, NJ: Prentice-Hall, 1985) and
[14] R. Hecht-Nielsen, Neurocomputing.
Reading, MA: Addison-Wesley,
Adaptive Inverse Control (Englewood Cliffs, NJ: Prentice-Hall, 1996). A new 1990.
book, Quantization Noise, is in preparation.