Results and perspectives on computational methods for optimal control of switched systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2623, Issue , 2003, Pages 540-555

  Xu, Xuping ^a   Antsaklis, Panos J ^b  

^a BEHREND COLLEGE   (United States)

^b University of Notre Dame   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HYBRID SYSTEMS; OPTIMAL CONTROL SYSTEMS; SURVEYS; SWITCHING SYSTEMS;

DISCRETIZATIONS; GENERAL MODEL; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; PAPER SURVEYS; RECENT PROGRESS; SWITCHED SYSTEM; TWO STAGE OPTIMIZATIONS;

COMPUTATIONAL METHODS;

EID: 35248899269     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36580-x_39     Document Type: Review

References (37)

1. A. Bemporad and M. Morari. Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3):407-427, March 1999.
2. A. Bemporad, F. Borrelli, and M. Morari. Optimal controllers for hybrid systems: stability and piecewise linear explicit form. Proc. 39th IEEE CDC, 1810-1815, 2000.
3. A. Bemporad, F. Borrelli, and M. Morari. On the optimal control law for linear discrete time hybrid systems. HSCC 2002, LNCS 2289, 105-109, Springer, 2002.
4. D.P. Bertsekas. Nonlinear Programming, Second Edition. Athena Scientific, 1999.
5. M.S. Branicky, V.S. Borkar, and S.K. Mitter. A unified framework for hybrid control: model and optimal control theory. IEEE Trans. on AC, 43(1):31-45, January 1998.
6. C.G. Cassandras, D.L. Pepyne, and Y. Wardi. Optimal control of a class of hybrid systems. IEEE Trans. on AC, 46(3):398-415, March 2001.
7. A. Giua, C. Seatzu, and C. Van Der Mee. Optimal control of autonomous linear systems switched with a pre-assigned finite sequence. Proc. 2001 IEEE ISIC, 144-149, 2001.
8. A. Giua, C. Seatzu, and C. Van Der Mee. Optimal control of switched autonomous linear systems. Proc. 40th IEEE CDC, 2472-2477, 2001.
9. K. Gokbayrak and C.G. Cassandras. A hierarchical decomposition method for optimal control of hybrid systems. Proc. 39th IEEE CDC, 2472-2477, 2000.
10. K. Gokbayrak and C.G. Cassandras. Hybrid controllers for hierarchically decomposed systems. HSCC 2000, LNCS 1790, 117-129, Springer, 2000.
11. S. Hedlund and A. Rantzer. Optimal control of hybrid system. Proc. 38th IEEE CDC, 3972-3977, 1999.
12. S. Hedlund and A. Rantzer. Convex dynamic programming for hybrid systems. IEEE Trans. on AC, 47(9):1536-1540, September 2002.
13. F.L. Lewis. Optimal Control. Wiley Interscience, 1986.
14. B. Lincoln and B.M. Bernhardsson. Efficient pruning of search trees in LQR control of switched linear systems. Proc. 39th IEEE CDC, 1828-1833, 2000.
15. J. Lu, L. Liao, A. Nerode, and J.H. Taylor. Optimal control of systems with continuous and discrete states. Proc. 32nd IEEE CDC, 2292-2297, 1993.
16. B. Ma. An improved algorithm for solving constrained optimal control problems. Ph.D. Thesis, University of Maryland, 1994.
17. S.G. Nash and A. Sofer. Linear and Nonlinear Programming. McGraw-Hill, 1996.
18. D.L. Pepyne and C.G. Cassandras. Modeling, analysis, and optimal control of a class of hybrid systems. DEDS: Theory and Applications, Vol. 8, 175-201, 1998.
19. D.L. Pepyne and C.G. Cassandras. Optimal control of hybrid systems in manufacturing. Proceedings of the IEEE, 88(7):1108-1123, July 2000.
20. B. Piccoli. Hybrid systems and optimal control. Proc. 37th IEEE CDC, 13-18, 1998.
21. E. Polak. An historical survey of computational methods in optimal control. SIAM Review, 15(2):553-584, April 1973.
22. A. Rantzer and M. Johansson. Piecewise linear quadratic optimal control. IEEE Trans. on AC, 45(4):629-637, April 2000.
23. th IEEE CDC, 3059-3064, 1999.
24. P. Riedinger, C. Zanne, and F. Kratz. Time optimal control of hybrid systems. Proc. 1999 ACC, 2466-2470, 1999.
25. T.I. Seidman. Optimal control for switching systems. Proc. 21st Annual Conf. on Infor. Sci. and Sys., 485-489, 1987.
26. H.J. Sussmann. A maximum principle for hybrid optimal control problems. Proc. 38th IEEE CDC, 425-430, 1999.
27. L.Y. Wang, A. Beydoun, J. Cook, J. Sun, and I. Kolmanovsky. Optimal hybrid control with applications to automotive powertrain systems. LNCIS 222, 190-200, Springer, 1997.
28. H.S. Witsenhausen. A class of hybrid-state continuous-time dynamic systems. IEEE Trans. on AC, 11(2):161-167, April 1966.
29. X. Xu and P.J. Antsaklis. Optimal control of switched systems: new results and open problems. Proc. 2000 ACC, 2683-2687, 2000.
30. X. Xu. Analysis and design of switched systems. Ph.D. Thesis, University of Notre Dame, August 2001. Also available at: http://ece.bd.psu.edu/~xu/
31. X. Xu and P.J. Antsaklis. An approach to optimal control of switched systems with internally forced switchings. Proc. 2002 ACC, 148-153, 2002.
32. X. Xu and P.J. Antsaklis. An approach to switched sytems optimal control based on parameterization of the switching instants. Proc. 15th IFAC World Congress, 2002.
33. X. Xu and P.J. Antsaklis. Optimal control of switched autonomous systems. Proc. 41st IEEE CDC, 4401-4406, 2002.
34. X. Xu and P.J. Antsaklis. Optimal control of switched systems via nonlinear optimization based on direct differentiations of value functions. Int. J. of Control, 75(16/17):1406-1426, 2002.
35. X. Xu and P.J. Antsaklis. Optimal control of switched systems based on parameterization of the switching instants. IEEE Trans. on AC, accepted, 2002.
36. X. Xu and P.J. Antsaklis. Optimal control of hybrid autonomous systems with state jumps. The 2003 ACC, submitted, 2002.
37. J. Yong. Systems governed by ordinary differential equations with continuous, switching and impulse controls. Appl. Math. Optim., 20:223-235, 1989.