Overlapping quadratic optimal control of linear time-varying commutative systems

SIAM Journal on Control and Optimization

Volumn 40, Issue 5, 2002, Pages 1611-1627

  Bakule, Lubomír ^a   Rodellar, José ^a   Rossell, Joseph M ^a  

^a INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Commutative systems; Decentralization; Inclusion principle; Large scale systems; Linear time varying continuous time systems; Optimal control; Overlapping decomposition; Suboptimality

Indexed keywords

DECENTRALIZED CONTROL; LARGE SCALE SYSTEMS; LINEAR SYSTEMS; MATRIX ALGEBRA; TIME VARYING SYSTEMS;

INCLUSION PRINCIPLE; LINEAR TIME-VARYING COMMUTATIVE SYSTEMS; OVERLAPPING QUADRATIC OPTIMAL CONTROL;

OPTIMAL CONTROL SYSTEMS;

EID: 0036407198     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012900367643     Document Type: Article

References (26)

1. M. Athans and P. L. Falb, Optimal Control, McGraw-Hill, New York, 1966.
2. L. Bakule and J. Rodellar, Decentralized control and overlapping decomposition of mechanical systems. Part 1: System decomposition. Part 2: Decentralized stabilization, Internat. J. Control, 61 (1995), pp. 559-587.
3. L. Bakule, J. Rodellar, and J. M. Rossell, Structure of expansion-contraction matrices in the inclusion principle for dynamic systems, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1136-1155.
4. L. Bakule, J. Rodellar, and J. M. Rossell, Generalized selection of complementary matrices in the inclusion principle, IEEE Trans. Automat. Control, 45 (2000), pp. 1237-1243.
5. B. Barán, E. Kaszkurewicz, and A. Bhaya, Parallel asynchronous team algorithms: Convergence and performance analysis, IEEE Trans. Parallel and Distributed Systems, 7 (1996), pp. 677-688.
6. Z. Drici, New directions in the method of vector Lyapunov functions, J. Math. Anal. Appl., 184 (1994), pp. 317-325.
7. A. Iftar, Decentralized optimal control with extensions, in Proceedings of the First IFAC Symposium on Design Methods of Control Systems, Zurich, Switzerland, 1991, pp. 747-752.
8. A. Iftar, Overlapping decentralized dynamic optimal control, Internat. J. Control, 58 (1993), pp. 187-209.
9. A. Iftar and E. J. Davison, A decentralized discrete-time controller for dynamic routing, Internat. J. Control, 69 (1998), pp. 599-632.
10. A. Iftar and Ü. Özgüner, Overlapping decompositions, expansions, contractions, and stability of hybrid systems, IEEE Trans. Automat. Control, 43 (1998), pp. 1040-1055.
11. M. Ikeda and D. D. Šiljak, Overlapping decompositions, expansions and contractions of dynamic systems, Large Scale Systems, 1 (1980), pp. 29-38.
12. M. Ikeda, D. D. Šiljak, and D. E. White, Decentralized control with overlapping information sets, J. Optim. Theory Appl., 34 (1981), pp. 279-310.
13. M. Ikeda, D. D. Šiljak, and D. E. White, An inclusion principle for dynamic systems, IEEE Trans. Automat. Control, 29 (1984), pp. 244-249.
14. M. Ikeda, D. D. Šiljak, and D. E. White, Overlapping decentralized control of linear time-varying systems, in Advances in Large Scale Systems, Vol. 1, JAI Press, Greenwich, CT, 1984, pp. 93-116.
15. H. Ito, Overlapping decomposition for multirate decentralized control, in Preprints of the 8th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, Patras, Greece, 1998, 259-264.
16. E. W. Kamen, Fundamentals of linear time-varying systems, in The Control Handbook, CRC Press, Boca Raton, FL, 1996, pp. 451-467.
17. W. S. Levine, T. L. Johnson, and M. Athans, Optimal limited state variable feedback controllers for linear systems, IEEE Trans. Automat. Control, 16 (1971), pp. 785-793.
18. ∞ control of linear time-varying systems: A state-space approach, SIAM J. Control Optim., 29 (1991), pp. 1394-1413.
19. J. M. Rossell, Contribution to Decentralized Control of Large-Scale Systems via Overlapping Models, Ph.D. thesis, Technical University of Catalunya, Barcelona, Spain, 1998 (in Spanish).
20. W. J. Rugh, Linear System Theory, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 1996.
21. M. E. Sezer and D. D. Šiljak, Nested epsilon decompositions of linear systems: Weakly coupled and overlapping blocks, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 521-533.
22. D. D. Šiljak, Decentralized Control of Complex Systems, Academic Press, New York, 1991.
23. D. D. Šiljak, S. M. Mladenović, and S. Stanković, Overlapping decentralized observation and control of a platoon of vehicles, in Proceedings of the American Control Conference, San Diego, CA, 1999, pp. 4522-4526.
24. S. S. Stanković, X. B. Chen, and D. D. Šiljak, Stochastic inclusion principle applied to decentralized automatic generation control, Internat. J. Control, 72 (1999), pp. 276-288.
25. M. Y. Wu and A. Sherif, On the commutative class of linear time-varying systems, Internat. J. Control, 23 (1976), pp. 433-444.
26. A. I. Zečevič and D. D. Siljak, A block-parallel Newton method via overlapping epsilon decompositions, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 824-844.