The optimal projection equations for reduced-order, discrete-time modeling, estimation, and control

Journal of Guidance, Control, and Dynamics

Volumn 9, Issue 3, 1986, Pages 288-293

  Bernstein, D S ^a,b   Davis, L D ^a,b   Hyland, D C ^a,b  

^a National Center for Health Statistics   (United States)

^b Government Aerospace Systems Division ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS, OPTIMAL; SIGNAL FILTERING AND PREDICTION - KALMAN FILTERING;

LQG CONTROL; OPTIMAL PROJECTION EQUATIONS; STATE ESTIMATION;

CONTROL SYSTEMS, DISCRETE TIME;

EID: 0022715577     PISSN: 07315090     EISSN: None     Source Type: Journal    
DOI: 10.2514/3.20105     Document Type: Article

References (46)

1. Hyland, D.C., “Optimality Conditions for Fixed-Order Dynamic Compensation of Flexible Spacecraft with Uncertain Parameters,” 1982.
2. Hyland, D.C. and Madiwale, A.N., “Fixed-Order Dynamic Compensation Through Optimal Projection,”Proceedings of the Workshop on Applications of Distributed System Theory to the Control of Large Space Structures, edited by G. Rodriguez, Jet Propulsion Laboratory, Pasadena, CA, 1982, pp. 409-427.
3. Hyland, D.C. “Mean-Square Optimal Fixed-Order Compensation —Beyond Spillover Suppression,” 1982.
4. Hyland, D.C., “The Optimal Projection Approach to Fixed-Order Compensation: Numerical Methods and Illustrative Results,” 83-0303, 1983.
5. Hyland, D.C. and Bernstein, D.S., “Explicit Optimality Conditions for Fixed-Order Dynamic Compensation,”Proceedings of the 22nd IEEE Conference on Decision and Control, San Antonio, TX, 1983, pp. 161-165.
6. Hyland, D.C., “Comparison of Various Controller-Reduction Methods: Suboptimal Versus Optimal Projection,”Proceedings of the AIAA Dynamics Specialists Conference, Palm Springs, CA, 1984, pp. 381-389.
7. Hyland, D.C. and Bernstein, D.S., “The Optimal Projection Equations for Fixed-Order Dynamic Compensation,”IEEE Transactions on Automatic Control, Vol. AC29, 1984, pp. 1034-1037.
8. Hyland, D.C. and Bernstein, D.S. “The Optimal Projection Approach to Model Reduction and the Relationship Between the Methods of Wilson and Moore,”Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, NV, 1984, pp. 120-126.
9. Bernstein, D.S. and Hyland, D.C., “The Optimal Projection Equations for Reduced-Order State Estimation,”IEEE Transactions on Automatic Control, Vol. AC30,1985, pp. 583-585.
10. Hyland, D.C. and Bernstein, D.S., “The Optimal Projection Equations for Model Reduction and the Relationships Among the Methods of Wilson, Skelton and Moore,”IEEE Transactions on Automatic Control, to appear.
11. Bernstein, D.S. and Hyland, D.C., “The Optimal Projection Equations for Finite-Dimensional Fixed-Order Dynamic Compensation of Infinite-Dimensional Systems,”SIAM Journal on Control and Optimization, to appear.
12. Looze, D.P. and Sandell, N. R. “Gradient Calculations for Linear Quadratic Fixed Control Structure Problems,”IEEE Transactions on Automatic Control, Vol. AC25,1980, pp. 258-285.
13. Skelton, R.E., “Cost Decomposition of Linear Systems with Application to Model Reduction,”International Journal on Control, Vol. 32, 1980, pp. 1031-1055.
14. Skelton, R.E. and Yousuff, A., “Component Cost Analysis of Large Scale Systems,”International Journal on Control, Vol. 37, 1983, pp. 285-304.
15. Yousuff, A. “Controller Reduction by Component Cost Analysis,”IEEE Transactions on Automatic Control, Vol. AC29, 1984, pp. 520-530.
16. Mitra, D., “Analytical Results on the Use of Reduced Models in the Control of Linear Dynamical Systems,”Proceedings of IEE, Vol. 116, 1969, pp. 1439-1444.
17. Wilson, D.A., “Optimum Solution of Model-Reduction Problem,”Proceedings of IEE, Vol. 117,1970, pp. 1161-1165.
18. Applevich, J.D., “Approximation of Discrete Linear Systems,”International Journal on Control, Vol. 17,1973, pp. 565-575.
19. Wilson, D.A., “Model Reduction for Multivariable Systems,”International Journal on Control, Vol. 20,1974, pp. 57-64.
20. Hickin, J. and Sinha, N.K., “Applications of Projective Reduction Methods to Estimation and Control,”Journal on Cybernetics, Vol. 8, 1978, pp. 159-181.
21. Mishra, R.N. and Wilson, D.A., “A New Algorithm for Optimal Reduction of Multivariable Systems,”International Journal on Control, Vol. 31,1980, pp. 443-466.
22. Kabamba, P.T., “Model Reduction by Euclidean Methods,”Journal of Guidance and Control, Vol. 3,1980, pp. 555-562.
23. Moore, B.C., “Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction,”IEEE Transactions on Automatic Control, Vol. AC26,1981, pp. 17-32.
24. Eitelberg, E., “Model Reduction by Minimizing the Weighted Equation Error,”International Journal on Control, Vol. 34, 1981, pp. 1113-1123.
25. Sims, C.S., “Reduced-Order Modelling and Filtering,”Control and Dynamic Systems, Vol. 18, edited by C.T. Leondes, 1982, pp. 55-103.
26. Simon, K.W. and Stubberud, A.R., “Reduced Order Kalman Filter,”International Journal on Control, Vol. 10,1969, pp. 501-509.
27. Sims, C.S. “Specific Optimal Estimation,”IEEE Transactions on Automatic Control, Vol. AC14,1969, pp. 183-186.
28. Asher, R.B., Herring, K.D., and Ryles, J.C., “Bias Variance and Estimation Error in Reduced Order Filters,”Automatica, Vol. 12, 1976, pp. 589-600.
29. Galdos, J.I. “Information and Distortion in Reduced-Order Filter Design,”IEEE Transactions on Information Theory, Vol. IT23, 1977, pp. 183-194.
30. Sims, C.S. “Optimal and Suboptimal Results in Full- and Reduced-Order Linear Filtering,”IEEE Transactions on Automatic Control, Vol. AC23,1978, pp. 469-472.
31. Wilson, D.A. and Mishra, R.N., “Design of Low Order Estimators Using Reduced Models,”International Journal on Control, Vol. 23, 1979, pp. 447-456.
32. Dombrovskii, U.V., “Method of Synthesizing Suboptimal Filters of Reduced Order for Digital Linear Dynamic Systems,”Automation and Remote Control, Vol. 43,1982, pp. 1483-1489.
33. Levine, W.S., Johnson, T.L. “Optimal Limited State Variable Feedback Controllers for Linear Systems,”IEEE Transactions on Automatic Control, Vol. AC16,1971, pp. 785-793.
34. Kwakemaak, K. and Sivan, R, Linear Optimal Control Systems, Wiley-Interscience, New York, 1972.
35. Sidar, M. and Kurtaran, B.Z., “Optimal Low-Order Controllers for Linear Stochastic Systems,”International Journal on Control, Vol. 22, 1975, pp. 377-387.
36. Mendel, J.J. “On the Design of Optimal Time-Invariant Compensators for Linear Stochastic Time-Invariant Systems,”IEEE Transactions on Automatic Control, Vol. AC20,1975, pp. 653-657.
37. Basuthakur, S. “Optimal Constant Controllers for Stochastic Linear Systems,”IEEE Transactions on Automatic Control, Vol. AC20, 1975, pp. 664-666.
38. Asher, R.B. “Linear Discrete Stochastic Control with a Reduced-Order Dynamic Compensator,”IEEE Transactions on Automatic Control, Vol. AC21, 1976, pp. 626-627.
39. Naeije, W.J. and Bosgra, O.H., “The Design of Dynamic Compensators for Linear Multivariable Systems,” IFAC, Fredricton, Canada, pp. 205-212.
40. Wenk, C.J. “Parameter Optimization in Linear; Systems with Arbitrarily Constrained Controller Structure,”IEEE Transactions on Automatic Control, Vol. AC25, 1980, pp. 496-500.
41. O’Reilly, J. “Optimal Low-Order Feedback Controllers for Linear Discrete-Time Systems,”Control and Dynamic Systems, Vol. 16, edited by C.T. Leondes, Academic Press, New York, 1980, pp. 335-367.
42. Grimble, M.J., “Reduced-Order Optimal Controller for DiscreteTime Stochastic Systems,”Proceedings of IEE, Vol. 127, 1980, pp. 55-63.
43. Kabamba, P.T. and Longman, R.W., “An Integrated Approach to Reduced-Order Control Theory,”Optimal Control Applications and Methods, Vol. 4, 1983, pp. 405-415.
44. Kato, T., Perturbation Theory for Linear Operators,2nd Ed., Springer-Verlag, New York, 1976.
45. Rao, C.R. and Mitra, S.K., Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, New York, 1971.
46. Van Loan, C.F., “Computing Integrals Involving the Matrix Exponential,”IEEE Transactions on Automatic Control, Vol. 23,1978, pp. 395-404.