H∞-differential Riccati equations: Convergence properties and finite escape phenomena

IEEE Transactions on Automatic Control

Volumn 42, Issue 1, 1997, Pages 113-118

  Bolzern, P ^a   Colaneri, P ^a   De Nicolao, G ^b  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF PAVIA   (Italy)

Author keywords

Differential games; Finite escapes; Finite horizon robust control; H filtering and control; Riccati equations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; PERFORMANCE; RICCATI EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS);

BOUNDEDNESS; DIFFERENTIAL GAMES; DIFFERENTIAL RICCATI EQUATIONS; FINITE ESCAPE PHENOMENA;

CONTROL THEORY;

EID: 0030785256     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.553694     Document Type: Article

References (21)

1. R. E. Kalman, "New methods in Wiener filtering theory," in Proc. 1st Symp. Eng. Appl. Random Function Th. Prob., 29, J. Bogdanoff and F. Kozin, Eds. Wiley, 1963, pp. 70-388.
2. M. A. Shayman, "Phase portrait of the matrix Riccati equation," SIAM J. Contr. Opt., vol. 24, pp. 1-65, 1986.
3. S. Bittanti, A. J. Laub, and J. C. Willems, Eds., The Riccati Equation. Berlin: Springer, 1990.
4. ∞ control problems," IEEE Trans. Automat. Contr., vol. 34, pp. 831-847, 1989.
5. ∞-norm sense," in Proc. 28th Conf. Decision Contr., Tampa, FL, Dec. 1989, pp. 421-425.
6. ∞ - Optimal Control and Related Minimax Design Problems - A Dynamic Game Approach. Boston: Birkäuser, 1991.
7. ∞ control with transients," SIAM J. Cont. Optimiz., vol. 29, pp. 1373-1393, 1991.
8. ∞ control of linear time-varying systems: A state space approach," SIAM J. Cont. Optimiz., vol. 29, pp. 1394-1413, 1991.
9. ∞ setting," IEEE Trans. Automat. Contr., vol. 36, pp. 152-166, 1991.
10. ∞ control for time-varying systems," SIAM J. Contr. Optimiz., vol. 30, pp. 262-283, 1992.
11. ∞ filtering for continuous time-varying uncertain systems with deterministic input signals," IEEE Trans. Sig. Proc., vol. 43, pp. 709-719, 1992.
12. ∞ optimal estimation: A tutorial," in Proc. 31st Conf. Decision Contr., Tucson, AZ, Dec. 1992, pp. 2278-2286.
13. ∞ control problems with terminal penalties," IEEE Trans. Automat. Contr., vol. 37, pp. 1762-1767, 1992.
14. G. Freiling, G. Jank, S. R. Lee, and H. Abou-Kandil, "On the global existence of solutions for game Riccati differential equations," in Proc. 3rd Europ. Contr. Conf., Rome, Italy, Sept. 1995, pp. 2597-2602.
15. T. Sasagawa, "On the finite escape phenomena for matrix Riccati equations," IEEE Trans. Automat. Contr., vol. AC-27, pp. 977-979, 1982.
16. P. E. Crouch and M. Pavon, "On the existence of solutions of the Riccati differential equation," Syst. Contr. Lett., vol. 9, pp. 203-206, 1987.
17. G. Tadmor, "Receding horizon revisited: An easy way to robustly stabilize an LTV system," Syst. Contr. Lett., vol. 18, pp. 285-294, 1992.
18. S. Lall and K. Glover, "A game theoretic approach to moving horizon control," in Advances in Model-Based Predictive Control, D. W. Clarke Ed. Oxford: Oxford Univ. Press, 1994, pp. 131-144.
19. ∞-differential Riccati equation," in Proc. IFAC Word Congr., San Francisco, CA, July 1996, vol. G, pp. 161-166.
20. G. De Nicolao and M. Gevers, "Difference and differential Riccati equations: A note on the convergence to the strong solution," IEEE Trans. Automat. Contr., vol. 37, pp. 1055-1057, 1992.
21. ∞ Riccati solutions," in Proc. 30th Conf. Decision Contr., Brighton, England, Dec. 1991, pp. 1927-1932.