Convex design control for practical nonlinear systems

IEEE Transactions on Automatic Control

Volumn 59, Issue 7, 2014, Pages 1692-1705

  Baldi, Simone ^a,b   Michailidis, Iakovos ^c   Kosmatopoulos, Elias B ^b,c   Papachristodoulou, Antonis ^d   Ioannou, Petros A ^e  

^a UNIVERSITY OF CYPRUS   (Cyprus)

^b INFORMATION TECHNOLOGIES INSTITUTE   (Greece)

^c DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

^d UNIVERSITY OF OXFORD   (United Kingdom)

^e University of Southern California ^*  (United States)

Author keywords

Approximately optimal control (AOC); Control Lyapunov function (CLF); Convex control design (ConvCD); Semi definite programming (SDP)

Indexed keywords

CONTROL; CONVEX OPTIMIZATION; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS;

CONTROL DESIGN; CONTROL LYAPUNOV FUNCTION; CONTROL SCHEMES; FIXED COMPLEXITY; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLLER; OPTIMAL CONTROLS; SEMI-DEFINITE PROGRAMMING;

CONTROLLERS;

EID: 84903275703     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2014.2309271     Document Type: Article

References (31)

1. R. Bellman, Dynamic Programming. Princeton, NJ: Princeton University Press, 1957
2. A. J. van der Schaft, "l2-gain analysis of nonlinear systems and nonlinear state feedback H∞ control," IEEE Trans. Automat. Contr., vol. 37, pp. 770-784, 1992
3. A. Isidori andW. Kang, "H∞ control via measurement feedback for general nonlinear systems," IEEE Trans. Automat. Contr., vol. 40, pp. 466-472, 1995
4. T. Basar and P. Bernhard, H∞-Optimal Control and Related Minimax Design Problems. Boston, MA: Birkhauser, 1995
5. W. M. Lu and J. C. Doyle, " H∞ control of nonlinear systems: A convex characterization," IEEE Trans. Automat. Contr., vol. 40, pp. 1668-1675, 1995
6. M. R. James and J. S. Baras, "Partial observed differential games, infinitedimensional hamilton-jacobi-isaac equations, nonlinear H∞ control," SIAM J. Contr. Optimiz., vol. 34, pp. 1342-1364, 1996 (Pubitemid 126562717)
7. H. Chen and F. Allgower, "A quasi-infinite horizon nonlinearmodel predictive control scheme with guaranteed stability," Automatica, vol. 14, pp. 1205-1217, 1998 (Pubitemid 128431629)
8. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Stability and optimality," Automatica, vol. 36, pp. 789-814, 2000 (Pubitemid 30587683)
9. L. Magni, G. De Nicolao, L. Magnani, and R. Scattolini, "A stabilizing model-based predictive control for nonlinear systems," Automatica, vol. 37, pp. 1351-1362, 2001 (Pubitemid 32691030)
10. R. A. Freeman and P. V. Kokotovic, "Inverse optimality in robust stabilization," SIAM J. Contr. Optim., vol. 34, pp. 1365-1391, 1996 (Pubitemid 126562718)
11. M. Krstic and Z-H. Li, "Inverse optimal design of input-To-state stabilizing nonlinear controllers," IEEE Trans. Automat. Contr., vol. 43, pp. 336-350, 1998 (Pubitemid 128737353)
12. D. Bertsekas and J. Tsitsiklis, Neuro-Dynamic Programming. Athena Scientific, 1996
13. R. Beard, G. Saridis, and J. Wen, "Galerkin approximations of the generalized hamilton-jacobi-bellman equation," Automatica, vol. 33, pp. 2159-2177, 1997
14. R. Beard, G. Saridis, and J. Wen, "Approximate solutions to the timeinvariant hamilton-jacobi-bellman equation," Journal of Optimization Theory and Application, vol. 96, pp. 589-626, 1998
15. T. Parisini and R. Zoppoli, "Neural approximations for infinite horizon optimal control of nonlinear stochastic systems," IEEE Trans. Neural Networks, vol. 9, pp. 1388-1408, 1998 (Pubitemid 128742417)
16. M. Abu-Khalaf and F. L. Lewis, "Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach," Automatica, vol. 41, pp. 779-791, 2005 (Pubitemid 40352391)
17. E. B. Kosmatopoulos, "CLF-based control design with good transient performance for known and unknown multi-input nonlinear systems," in Proceedings of the European Control Conference, Budapest, Hungary, 2008
18. E. B. Kosmatopoulos, "Control of unknown nonlinear systems with efficient transient performance using concurrent exploitation and exploration," IEEE Trans. Neural Networks, vol. 21, pp. 1245-1261, 2010
19. E. B. Kosmatopoulos, "CLF-based control design for unknown multiinput nonlinear systems with good transient performance," IEEE Trans. Automatic Control, vol. 11, pp. 1245-1261, 2010
20. A. Rantzer and M. Johansson, "Piecewise linear quadratic optimal control," IEEE Trans. Automatic Control, vol. 45, pp. 629-637, 2000
21. S. Prajna, A. Papachristodoulou, and F. Wu, "Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach," in Proceedings of the Asian Control Conference, 2004
22. M. Johansson and A. Rantzer, "Computation of piecewise quadratic lyapunov functions for hybrid systems," IEEE Trans. Automatic Control, vol. 43, pp. 555-559, 1998 (Pubitemid 128737378)
23. L. Rodrigues, "Stability analysis of piecewise-Affine systems using controlled invariant sets," Systems & Control Letters, vol. 53, pp. 157-169, 2004
24. K. M. Passino and S. Yurkovich, Fuzzy Control. Menlo Park, CA: Addison Wesley Longman, 1998
25. F. D. Torrisi and A. Bemporad, "Hysdel-A tool for generating computational hybrid models," IEEE Trans. Control Systems Technology, vol. 43, pp. 336-350, 2003
26. A. Papachristodoulou and S. Prajna, "Robust stability analysis of nonlinear hybrid systems," IEEE Trans. Automat. Contr., vol. 54, pp. 1037-1043, 2009
27. X-M. Wu, A. M-C. So, Z. Li, and S-Y. R Li, "Fast graph laplacian regularized kernel learning via semidefinite-quadratic-linear programming," in NIPS2009, 2009
28. C-C. Chien, Y. Zhang, and P. A. Ioannou, "Traffic density control for automated highway systems," Automatica, vol. 33, pp. 1273-1285, 1997 (Pubitemid 127433509)
29. A. Hegyi, B. De Schutter, and J. Hellendoorn, "Optimal coordination of variable speed limits to suppress shock waves," IEEE Trans. Intelligent Transportation Systems, vol. 6, pp. 102-112, 2005 (Pubitemid 40384792)
30. E. B. Kosmatopoulos, "Adaptive control design based on adaptive optimization principles," IEEE Trans. Automatic Control, vol. 53, pp. 2680-2685, 2008
31. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.