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TECHNICAL BRIEFS

Neighboring Optimal Feedback Law for Higher-Order Dynamic Systems

[+] Author and Article Information
Tawiwat Veeraklaew, Sunil K. Agrawal

Mechanical Systems Laboratory, Department of Mechanical Engineering, University of Delaware, Newark, DE 19716

J. Dyn. Sys., Meas., Control 124(3), 492-497 (Jul 23, 2002) (6 pages) doi:10.1115/1.1490130 History: Received January 26, 2000; Online July 23, 2002
Copyright © 2002 by ASME
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References

Isidori, A., 1995, Nonlinear Control Systems, 3rd edition, Springer-Verlag, New York.
Fliess,  M., Levine,  J., Martin,  P., and Rouchon,  P., 1995, “Flatness and Defect of Nonlinear Systems: Introductory Theory and Examples,” Int. J. Control, 61, (6) (pp. 1327–1361;).
Bryson Jr., A. E., and Ho, Y. C., 1975, Applied Optimal Control, Hemisphere, New York.
Kirk, D. E., 1970, Optimal Control Theory: An Introduction, Prentice Hall Electrical Engineering Series, Englewood Cliffs, NJ.
Agrawal,  S. K., and Veeraklaew,  T., 1996, “A Higher-Order Method for Dynamic Optimization of a Class of Linear Time-Invariant,” ASME J. Dyn. Syst., Meas., Control, 118, 4, pp. 786–791.
Agrawal,  S. K., and Faiz,  N., 1998, “A New Efficient Method for Optimization of a Class of Nonlinear Systems Without Lagrange Multipliers,” J. Optim. Theory Appl., 97, 1, pp. 11–28.
Veeraklaew,  T., and Agrawal,  S. K., 2001, “A New Computation Framework for Optimization of Higher-Order Dynamic Systems,” AIAA Journal of Guidance, Control, and Dynamics, 24, 2, pp. 228–236.
Anderson, B. O., and Moore, J. B., 1990, Optimal Control: Linear Quadratic Methods, Prentice-Hall, Englewood Cliffs, NJ, 1990.
Forsyth, A. R., 1960, Calculus of Variations, Dover Publications, New York.
Gelfand, I. S., and Fomin, S. V., 1963, Calculus of Variations, Prentice-Hall, Englewood Cliffs, NJ.
Veeraklaew, T., 2000, Extensions of Optimization Theory and New Computational Approaches for Higher-Order Dynamic Systems, Ph.D. thesis, Dept. of Mechanical Engineering, University of Delaware.
Stadler, W., 1995, Analytical Robotics and Mechatronics, McGraw-Hill, New York.

Figures

Grahic Jump Location
A schematic of the on-line implementation of the neighboring optimal procedure to modify the optimal path for small perturbations in the initial conditions
Grahic Jump Location
One-link manipulator with friction
Grahic Jump Location
Optimal and neighboring optimal trajectories of the manipulator link from θ1(0)=1.5,θ1(0)=1.55 to the vertically down position
Grahic Jump Location
A spring-mass-damper system with two masses and one input
Grahic Jump Location
The optimal and neighboring optimal (i) inputs, (ii) states for Example 2

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