Discrete-time inverse optimal control for block control form nonlinear systems

World Automation Congress Proceedings

Volumn , Issue , 2012, Pages

  Ornelas Tellez, Fernando ^a   Sanchez, Edgar N ^b   Loukianov, Alexander G ^b  

^a UNIVERSIDAD MICHOACANA DE SAN NICOLÁS DE HIDALGO   (Mexico)

^b UNIDAD GUADALAJARA   (Mexico)

Author keywords

block control form systems; control Lyapunov function; Inverse optimal control; nonlinear systems

Indexed keywords

BLOCK CONTROL; CONTROL LYAPUNOV FUNCTION; CONTROL SCHEMES; DISCRETE-TIME CONTROL; DISCRETE-TIME NONLINEAR SYSTEMS; HAMILTON-JACOBI-BELLMAN EQUATIONS; INVERSE-OPTIMAL CONTROL; OPTIMAL CONTROLLER; TRAJECTORY TRACKING; UNSTABLE SYSTEM;

LYAPUNOV METHODS;

NONLINEAR SYSTEMS;

EID: 84870776222     PISSN: 21544824     EISSN: 21544832     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. R. Sepulchre, M. Jankovic, and P. V Kokotovic, Constructive Nonlinear Control. London, New York, USA: Springer-Verlag, 1997.
2. M. Krstic and H. Deng, Stabilization of Nonlinear Uncertain Systems. Secaucus, NJ, USA: Springer-Verlag New York, Inc., 1998.
3. B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods. Englewood Cliffs, New Jersey, USA: Prentice-Hall, 1990.
4. R. E. Kalman, "When is a linear control system optimal?" Transactions of the ASM E, Journal of Basic Engineering, Series D, vol. 86, pp. 81-90, 1964.
5. R. A. Freeman and P. V Kokotovic, "Optimal nonlinear controllers for feedback linearizable systems," in Proceedings of the 14th American Control Coriference, 1995, vol. 4, Seattle, WA, USA, June 1995, pp. 2722-2726.
6. P. J. Moylan and B. D. O. Anderson, "Nonlinear regulator theory and an inverse optimal control problem," IEEE Transactions on Automatic Control, vol. 18, no. 5, pp. 460-465, 1973.
7. J. L. Willems and H. V D. Voorde, "Inverse optimal control problem for linear discrete-time systems," Electronics Letters, vol. 13, p. 493, Aug 1977.
8. L. Magni and R. Sepulchre, "Stability margins of nonlinear receding horizon control via inverse optimality," Systems and Control Letters, vol. 32, no. 4, pp. 241-245, 1997. [Online]. Available: http://www.montefiore.ulg.ac. be/services/stochastic/pubsl-19971M-S97
9. R. A. Freeman and P. V Kokotovic, Robust nonlinear control design: state-space and Lyapunov techniques. Cambridge, MA, USA: Birkhauser Boston Inc., 1996.
10. T. Ahmed-Ali, F. Mazenc, and F. Lamnabhi-Lagarrigue, "Disturbance attenuation for discrete-time feedforward nonlinear systems," Lecture notes in control and iriformation sciences, vol. 246, pp. 1-17, March 1999.
11. F. Ornelas, E. N. Sanchez, and A. G. Loukianov, "Discrete-time inverse optimal control for nonlinear systems trajectory tracking," in Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, Georgia, USA, Dec 2010, pp. 4813-4818.
12. R. A. Freeman and P. V Kokotovic, "Inverse optimality in robust stabilization," SIAM Journal on Control and Optimization, vol. 34, no. 4, pp. 1365-1391, 1996.
13. J. A. Primbs, V Nevistic, and J. C. Doyle, "Nonlinear optimal control: A control Lyapunov function and receding horizon perspective," Asian Journal of Control, vol. I, pp. 14-24, 1999.
14. R. A. Freeman and J. A. Primbs, "Control Lyapunov functions: New ideas from an old source," in Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, 1996, pp. 3926-3931.
15. D. E. Kirk, Optimal Control Theory: An Introduction. Prentice-Hall, NJ, USA, 1970.
16. F. L. Lewis and V L. Syrmos, Optimal control. John Wiley & Sons, New York, USA, 1995.
17. T. Basar and G. J. Olsder, Dynamic noncooperative game theory, 2nd ed. Academic Press, New York, 1995.
18. A. Al-Tamimi and F. L. Lewis, "Discrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proof," IEEE Transactions on Systems, Man, Cybernetics-Part B, vol. 38, no. 4, pp. 943-949, August 2008.
19. T. Ohsawa, A. M. Bloch, and M. Leok, "Discrete Hamilton-Jacobi theory," 2009. [Online]. Available: http://www.citebase.org/abstract?id= oai:arXiv.org:0911.2258
20. W. M. Haddad, V-So Chellaboina, J. L. Fausz, and C. Abdallah, "Optimal discrete-time control for non-linear cascade systems," Journal of The Franklin Institute, vol. 335, no. 5, pp. 827-839, 1998.
21. H. K. Khalil, Nonlinear Systems. New Jersey: Prentice Hall, 1996.
22. G. L. Amicucci, S. Monaco, and D. Normand-Cyrot, "Control Lyapunov stabilization of affine discrete-time systems," vol. 1, San Diego, CA, USA, Dec. 1997, pp. 923-924.
23. M. Vidyasagar, Nonlinear systems analysis, 2nd ed. Prentice Hall, 1993.
24. A. G. Loukianov, "Nonlinear block control with sliding modes," Automation and Remote Control, vol. 57, no. 7, pp. 916-933, 1998.