Numerical algorithms and issues concerning the discrete-time optimal projection equations

European Journal of Control

Volumn 6, Issue 1, 2000, Pages 93-110

  Van Willigenburg, L G ^a   De Koning, W L ^b  

^a WAGENINGEN UNIVERSITY   (Netherlands)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Discrete time systems; Fixed order LQG control; Numerical algorithms; Optimal reduced order dynamic compensation

Indexed keywords

EID: 0002740141     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0947-3580(00)70917-4     Document Type: Article

References (20)

1. Liu Y, Anderson BDO. Controller reduction: concepts and approaches. IEEE Transactions on Automatic Control 34(8): pp 802-812
2. Hyland DC, Bernstein DS. The optimal projection equations for fixed-order dynamic compensation. IEEE Transactions on Automatic Control 1984; AC-29: 1034-1037
3. Bernstein DS, Davis LD, Hyland DC. The optimal projection equations for reduced-order discrete-time modeling, estimation and control. Journal of Guidance Control and Dynamics 1986; 9(3): 288-293
4. De Koning WL, De Waard H. Necessary and sufficient conditions for optimal fixed-order dynamic compensation of linear discrete-time systems. Proceedings 1st IFAC symposium on design methods of control systems. Zurich, Switzerland 1991
5. Haddad WM, Huang HH, Bernstein DS. Robust stability and performance via fixed-order dynamic compensation: The discrete-time case. IEEE Transactions on Automatic Control 1992; 38(5): 776-782
6. Richter S, A homotopy algorithm for solving the optimal projection equations for fixed-order dynamic compensation: existence, convergence and global optimality. Proceedings of American Control Conference, Minneapolis, MN, June 1987, pp 1527-1531
7. Richter SL, Collins EG. A homotopy algorithm for reduced-order compensator design using the optimal projection equation. Proceedings 28th Conference on Decision and Control, Tampa, Florida 1989
8. Athans M. The matrix minimum principle, Information and Control 1968; 11: 592-606
9. Bernstein DS, Hyland DC. Optimal projection equations for reduced-order modelling, estimation and control of linear systems with multiplicative white noise. Journal of Optimization Theory and Applications 1988; 58(3): 387-409
10. Rao CR, Mitra SK. Generalized inverse of matrices and its applications. Wiley, New York 1971
11. De Koning WL. Compensatability and optimal compensation of systems with white parameters. IEEE Transactions on Automatic Control 1992; 37(5): 579-588
12. Yousuff A, Skelton RE. A note on balanced controller reduction. IEEE Transactions on Automatic Control 1984; 29(3): 254-257
13. Van Willigenburg LG, De Koning WL. Minimal and non-minimal optimal fixed-order compensators for time-varying discrete-time systems, MRS report 98-6, Department of Agricultural Engineering and Physics, Wageningen University, The Netherlands. Automatica (accepted) 1998
14. Richter SL, DeCarlo RA. Continuation methods: theory and applications. IEEE Transactions on Automatic Control 1983; AC-28(6): 660-665
15. Geromel JC, Peres PLD, Souza SR. Convex analysis of output feedback control problems: robust stability and performance. IEEE Transactions on Automatic Control 1996; 41(7): 997-1003
16. Matlab reference guide, Mathworks Inc., 1996
17. Control system toolbox for use with Matlab, user's Guide. Mathworks Inc., 1996
18. De Koning WL, Van Willigenburg LG. Numerical algorithms and issues concerning the discrete-time optimal projection equations for systems with white parameters. Proceedings UKACC International Conference on CONTROL '98, 1-4 September 1998, Swansea,UK, 1998; 2: 1605-1610
19. Van Willigenburg LG, De Koning WL. Optimal reduced-order compensation of time-varying discrete-time systems with deterministic and white parameters. Automatica 1999; 35: 129-138
20. Bernstein DS, Haddad WM. Optimal projection equations for discrete-time fixed-order dynamic compensation of linear systems with multiplicative white noise. International Journal of Control 1987; 46(1): 65-73