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Sensitivity based trajectory following control damping methods
1.  McCoy School of Engineering, Midwestern State University, 3410 Taft Blvd., Wichita Falls, TX 76308, United States 
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W. Grantham and T. Vincent, "Modern Control Systems Analysis and Design," Wiley, New York, 1993. Google Scholar 
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W. Grantham, Trajectory following optimization by gradient transformation differential equations,, Proc. 42^{nd} IEEE Conf. on Decision and Control, (): 9. Google Scholar 
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W. Grantham, Some necessary conditions for steepest descent controllability, Proceedings of the 1^{st} American Controls Conference, Alexandria, VA, 1982. Google Scholar 
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D. McDonald and W. Grantham, Singular perturbation trajectory following methods for minmax differential games, in "Advances in Dynamic Game Theory and Applications" (eds. S. Jorgensen, T. Vincent, and M. Quincampoix), Birkhauser, Boston, 2006, 659678. Google Scholar 
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T. Vincent and W. Grantham, Trajectory following methods in control system design, Journal of Global Optimization, 23 (2002), 267282. doi: 10.1023/A:1016530713343. Google Scholar 
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T. Vincent, B. Goh and K. Teo, Trajectoryfollowing algorithms for minmax optimization problems, Journal of Optimization Theory and Application, 75 (1992), 501519. doi: 10.1007/BF00940489. Google Scholar 
[12] 
T. Vincent and W. Grantham, "Nonlinear and Optimal Control Systems," Wiley, New York, 1997. Google Scholar 
show all references
References:
[1] 
M. Ahmad and J. Osman, Robust sliding mode control for robot manipulator tracking problem using a proportionalintegral switching surface, Proc. of the Student Conference on Research and Development, Putrajaya, Malaysia, (2003), 2935. Google Scholar 
[2] 
M. Chen, Y. Hwang and M. Tomizuka, A state dependent boundary layer design for sliding mode control, IEEE Trans. Aut. Cont., 47 (2002), 16771681. doi: 10.1109/TAC.2002.803534. Google Scholar 
[3] 
M. Corless and G. Leitmann, Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE Trans. Aut., ac26 (1981), 11391134. Google Scholar 
[4] 
R. Figliola and D. Beasely, "Theory and Design for Mechanical Measurements," 4^{th} Edition, Wiley, New York, 2006. Google Scholar 
[5] 
B. Goh, Algorithms for unconstrained optimization via control theory , Journal of Optimization Theory and Applications, 92 (1997), 581604. doi: 10.1023/A:1022607507153. Google Scholar 
[6] 
W. Grantham and T. Vincent, "Modern Control Systems Analysis and Design," Wiley, New York, 1993. Google Scholar 
[7] 
W. Grantham, Trajectory following optimization by gradient transformation differential equations,, Proc. 42^{nd} IEEE Conf. on Decision and Control, (): 9. Google Scholar 
[8] 
W. Grantham, Some necessary conditions for steepest descent controllability, Proceedings of the 1^{st} American Controls Conference, Alexandria, VA, 1982. Google Scholar 
[9] 
D. McDonald and W. Grantham, Singular perturbation trajectory following methods for minmax differential games, in "Advances in Dynamic Game Theory and Applications" (eds. S. Jorgensen, T. Vincent, and M. Quincampoix), Birkhauser, Boston, 2006, 659678. Google Scholar 
[10] 
T. Vincent and W. Grantham, Trajectory following methods in control system design, Journal of Global Optimization, 23 (2002), 267282. doi: 10.1023/A:1016530713343. Google Scholar 
[11] 
T. Vincent, B. Goh and K. Teo, Trajectoryfollowing algorithms for minmax optimization problems, Journal of Optimization Theory and Application, 75 (1992), 501519. doi: 10.1007/BF00940489. Google Scholar 
[12] 
T. Vincent and W. Grantham, "Nonlinear and Optimal Control Systems," Wiley, New York, 1997. Google Scholar 
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