Discrete-time fake riccati equations for Kalman filtering and receding-horizon control

Control and Dynamic Systems

Volumn 76, Issue C, 1996, Pages 79-102

  De Nicolao, Giuseppe ^a   Bitmead, Robert R ^b   Gevers, Michel ^c  

^a UNIVERSITY OF PAVIA   (Italy)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955370377     PISSN: 00905267     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0090-5267(96)80016-8     Document Type: Article

References (27)

1. Clarke D.W., Mohtadi C., and Tuffs P.S. Generalized Predictive Control. Part 1: The basic algorithm. Automatica 23 (1987) 137-148
2. Kwon W.H., and Pearson A.E. On feedback stabilization of time-varying discrete linear systems. IEEE Transactions on Automatic Control AC-23 (1978) 479-481
3. Bitmead R.R., Gevers M.R., Petersen I.R., and Kaye R.J. Monotonicity and stabilizability properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples. Systems Control Lett. 5 (1985) 309-315
4. Gevers M.R., Bitmead R.R., Petersen I.R., and Kaye R.J. When is the solution of the Riccati equation stabilizing at every iteration?. In: Byrnes C.I., and Lindquist A. (Eds). Frequency Domain and State Space Methods for Linear Systems (1986), North-Holland 531-540
5. Poubelle M.A., Bitmead R.R., and Gevers M.R. Fake algebraic Riccati techniques and stability. IEEE Transactions on Automatic Control AC-33 (1988) 379-381
6. Bitmead R.R., Gevers M.R., and Wertz V. Adaptive Optimal Control. The Thinking Man's GPC (1990), Prentice-Hall International, Sydney
7. Clarke D.W., and Scattolini R. Constrained Receding Horizon Predictive Control. Proc. IEE-D 138 (1991) 347-354
8. De Nicolao G., and Scattolini R. Stability and output terminal constraints in predictive control. In: Clarke D. (Ed). Advances in Model-Based Predictive Control (1994), Oxford University Press 105-121
9. Mosca E., and Zhang J. Stable redesign of predictive control. Automatica 28 (1992) 1229-1233
10. Rawlings J.B., and Muske K.R. The stability of constrained receding horizon control. IEEE Transactions on Automatic Control AC-38 (1993) 1512-1516
11. De Nicolao G. Cyclomonotonicity and stabilizability properties of solutions of the difference periodic Riccati equation. IEEE Transactions on Automatic Control AC-37 (1992) 1405-1410
12. Yan W., and Bitmead R.R. Periodic receding horizon LQ regulators for discrete-time systems. Proc. 30th Conf. on Decision and Control. Brighton, England (1991) 2301-2306
13. de Souza C.E., Gevers M.R., and Goodwin G.C. Riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices. IEEE Transactions on Automatic Control AC-31 (1986) 831-838
14. Pappas T., Laub A.J., and Sandell N.R. On the numerical solution of the discrete-time algebraic Riccati equation. IEEE Transactions on Automatic Control AC-25 (1980) 631-641
15. de Souza C.E. On stabilizing properties of solutions of the Riccati difference equation. IEEE Transactions on Automatic Control AC-34 (1986) 1313-1316
16. Bittanti S. Deterministic and stochastic linear periodic systems. In: Bittanti S. (Ed). Time Series and Linear Systems (1986), Springer-Verlag, Berlin 141-182
17. Bittanti S., Colaneri P., and De Nicolao G. The difference periodic Riccati equation for the periodic prediction problem. IEEE Transactions on Automatic Control AC-33 (1988) 706-712
18. Anderson B.D.O., and Moore J.B. Detectability and Stabilizability of time-varying discrete-time linear systems. SIAM J. Control and Optimiz 19 (1981) 20-32
19. Poubelle M.A., Petersen I.R., Gevers M.R., and Bitmead R.R. A miscellany of results on an equation of Count J.F. Riccati. IEEE Transactions on Automatic Control AC-31 (1986) 651-654
20. De Nicolao G. On a fallacious conjecture about the stabilizability properties of solutions of the Riccati difference equation. Systems & Control Letters 14 (1990) 409-410
21. Bemporad A., Chisci L., and Mosca E. On the stabilizing property of SIORHC. Automatica 30 (1994) 2013-2015
22. Danyang L., and Xuanhuang L. Optimal state estimation without the requirement of a priori statistics information of the initial state. IEEE Transactions on Automatic Control AC-39 (1994) 2087-2091
23. De Nicolao G. Cyclomonotonicity, Riccati equations and periodic receding horizon control. Automatica 30 (1994) 1375-1388
24. Keerthi S.S., and Gilbert E.G. Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations. J. Optimiz. Th. and Appl. 57 (1988) 265-293
25. Campo P.J., and Morari M. Robust control of processes subject to saturation nonlinearities. Computers and Chem. Eng. 14 (1990) 343-358
26. Michalska H., and Mayne D.Q. Robust receding horizon control of constrained nonlinear systems. IEEE Transactions on Automatic Control AC-38 (1993) 1623-1633
27. Mayne D.Q., and Polak E. Optimization based design and control. Proc. 12th IFAC World Congress, Sydney, Australia vol. III (1993) 129-138