Relatively Optimal Control and Its Linear Implementation

IEEE Transactions on Automatic Control

Volumn 48, Issue 12, 2003, Pages 2151-2162

  Blanchini, Franco ^a   Pellegrino, Felice Andrea ^a  

^a UNIVERSITY OF UDINE   (Italy)

Author keywords

Constrained control; Dead beat control; Linear control; Optimal control

Indexed keywords

CONTROL THEORY; DEGREES OF FREEDOM (MECHANICS); DYNAMIC PROGRAMMING; FEEDBACK CONTROL; FUNCTIONS; IMPULSE RESPONSE; LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; STATE SPACE METHODS;

CONSTRAINED CONTROL; DEAD-BEAT CONTROL;

OPTIMAL CONTROL SYSTEMS;

EID: 0346055405     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.820070     Document Type: Article

References (27)

1. G. Basile and G. Marro, Controlled and Conditioned Invariants in Linear System Theory. Upper Saddle River, NJ: Prentice-Hall, 1992.
2. A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems," Automatica, vol. 38, no. 1, pp. 3-20, Jan. 2002.
3. A. Bemporad, F. Borrelli, and M. Morari, "Model predictive control based on linear programming - The explicit solution," IEEE Trans. Automat. Contr., vol. 47, pp. 1974-1985, Dec. 2002.
4. D. P. Bertsekas, Dynamic Programming and Optimal Control. Belmont, MA: Athena Scientific, 2000.
5. F. Blanchini, "Set invariance in control - A survey,"Automatica, vol. 35, no. 11, pp. 1747-1767, 1999.
6. F. Blanchini and S. Miani, "Any domain of attraction for a linear constrained system is a tracking domain of attraction," SIAM J. Control Optim., vol. 38, no. 3, pp. 971-994, 2000.
7. F. Blanchini, S. Miani, and F. A. Pellegrino, "Suboptimal receding-horizon control for continuous-time systems," IEEE Trans. Automat. Contr., vol. 48, pp. 1081-1086, June 2003.
8. F. Blanchini and M. Sznaier, "Persistent disturbance rejection via static state feedback," IEEE Trans. Automat. Contr., vol. 40, pp. 1127-1131, June 1995.
9. ∞ gain minimization: Dynamic versus static state feedback," in Proc. 35th Conf. Decision Control, 1996, pp. 2395-2400.
10. F. Blanchini, F. Mesquine, and S. Miani, "Constrained stabilization with assigned initial condition set," Int. J. Control, vol. 62, no. 3, pp. 601-617, 1995.
11. 1'-Optimal feedback controllers for MIMO discrete-time systems," IEEE Trans. Automat. Contr., vol. 32, pp. 314-322, Apr. 1987.
12. _, "Minimization of a regulated response to a fixed input," IEEE Trans. Automat. Contr., vol. 33, pp. 924-930, Oct. 1988.
13. C. E. Garcia, D. M. Prett, and M. Morari, "Model predictive control theory and practice - A survey," Automatica, vol. 25, no. 3, pp. 335-348, 1989.
14. P. O. Gutman and M. Cwikel, "An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded control and states," IEEE Trans. Automat. Contr., vol. AC-32, pp. 251-254, Mar. 1987.
15. D. Henrion, S. Tarbouriech, and V. Kucera, "Control of linear systems subject to input constraints: A polynomial approach," Automatica, vol. 37, no. 4, pp. 597-604, Apr. 2001.
16. S. S. Keerthi and E. G. Gilbert, "Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints," IEEE Trans. Automat. Contr., vol. AC-32, pp. 432-435, May 1987.
17. V. Kucera, Analysis and Design of Discrete Linear Control Systems. Upper Saddle River, NJ: Prentice-Hall, 1991.
18. D. Q. Mayne, "Control of constrained dynamic systems," Euro. J. Control, vol. 7, pp. 87-99, 2001.
19. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Stability and optimality," Automatica, vol. 36, pp. 789-814, 2000.
20. A. S. Sage and C. C. White, Optimum System Control. Upper Saddle River, NJ: Prentice-Hall, 1997.
21. ∞-induced norm under full state feedback," IEEE Trans. Automat. Contr., vol. 41, pp. 533-544, Apr. 1996.
22. 1 optimal controllers for linear systems," IEEE Trans. Automat. Control, vol. 40, pp. 698-690, Apr. 1995.
23. A. Saberi, A. Stoorvogel, and P. Sannuti, Control of Linear Systems with Regulation and Input Constraints. London, U.K.: Springer-Verlag, 2000.
24. 1 problem without zero interpolation," SIAM J. Control Optim., vol. 37, no. 6, pp. 1865-1873, 1999.
25. ∞ optimization approach to robust controller design," SIAM J. Control Optim., vol 33, no. 4, pp. 1086-1101, 1995.
26. E. Gilbert and K. Tan, "Linear systems with state and control constraints: The theory and the applications of the maximal output admissible sets," IEEE Trans. Automat. Contr., vol. 36, pp. 1008-1020, Sept. 1991.
27. D. C. Youla, H. A. Jabr, and J. J. Bongiorno, "Modern Wiener-Hopf design of optimal controllers, II. The multivariable case," IEEE Trans. Automat. Contr., vol. AC-21, pp. 319-338, Mar. 1976.