Control of constrained discrete-time systems with bounded ℓ2 gain

IEEE Transactions on Automatic Control

Volumn 54, Issue 5, 2009, Pages 1105-1111

  Goulart, Paul J ^a   Kerrigan, Eric C ^a   Alamo, Teodoro ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Constrained systems; Receding horizon control (RHC); Robust control; Robust optimization; Uncertain systems

Indexed keywords

AFFINE FUNCTION; BOUNDED DISTURBANCES; CONSTRAINED LINEAR SYSTEMS; CONSTRAINED SYSTEMS; CONSTRAINT SATISFACTION; CONTROL HORIZON; CONTROL LAWS; DECISION VARIABLES; DISCRETE TIME SYSTEM; EXISTING METHOD; FINITE HORIZONS; INFINITE HORIZONS; NUMERICAL EXAMPLE; POLICY OPTIMIZATION; PROBLEM SIZE; QUADRATIC COSTS; RECEDING HORIZON CONTROL; RECEDING HORIZON CONTROL (RHC); RECEDING HORIZON CONTROLLERS; ROBUST OPTIMIZATION; TIME STEP;

CLOSED LOOP CONTROL SYSTEMS; CONSTRAINED OPTIMIZATION; CONVEX OPTIMIZATION; DIGITAL CONTROL SYSTEMS; LINEAR SYSTEMS; NONLINEAR CONTROL SYSTEMS; QUADRATIC PROGRAMMING; ROBUST CONTROL; UNCERTAIN SYSTEMS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 67349108291     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2013002     Document Type: Article

References (24)

1. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Stability and optimality," Automatica, vol. 36, no. 6, pp. 789-814, Jun. 2000, Survey paper.
2. ∞ control with performance adaptation for constrained linear systems," Automatica vol. 42, no. 6, pp. 1033-1040, Jun. 2006.
3. ∞ control scheme through Lagrange duality," Int. J. Control, vol. 79, no. 3, pp. 239-248, Mar. 2006.
4. K. B. Kim, "Disturbance attenuation for constrained discrete-time systems via receding horizon controls," IEEE Trans. Automat. Control vol. 49, no. 5, pp. 797-801, May 2004.
5. ∞ control: Quadratic programming approach," Int. J. Control, Automat. Syst., vol. 1, no. 2, pp. 178-183, Jun. 2003.
6. ∞ predictive control for systems with input saturation," Proc. Inst. Elect. Eng. vol. 147, no. 2, pp. 153-158, Mar. 2000.
7. H. Chen, C. W. Scherer, and F. Allgöwer, "A game theoretic approach to nonlinear robust receding horizon control of constrained systems," in Proc. Amer. Control Conf., Albuquerque, NM, Jun. 1997, pp. 3073-3077.
8. ∞ control problem," Automatica vol. 37, no. 3, pp. 429-435, Mar. 2001.
9. L. Magni, G. De Nicolao, R. Scattolini, and F. Allgöwer, "Robust model predictive control for nonlinear discrete-time systems," Int. J. Robust Nonlin. Control, vol. 13, pp. 229-246, 2003.
10. C. V. Rao, "Moving Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-Time Systems," Ph.D. dissertation, University of Wisconsin, Madison, 2000.
11. ∞ optimal control problem," Automatica, vol. 42, no. 3, pp. 371-382, Mar. 2006.
12. P. O. M. Scokaert and D. Q. Mayne, "Min-max feedback model predictive control for constrained linear systems," IEEE Trans. Automat. Control, vol. 43, no. 8, pp. 1136-1142, Aug. 1998.
13. P. J. Goulart, E. C. Kerrigan, and J. M. Maciejowski, "Optimization over state feedback policies for robust control with constraints," Automatica, vol. 42, no. 4, pp. 523-533, Apr. 2006.
14. A. Ben-Tal, A. Goryashko, E. Guslitzer, and A. Nemirovski, "Adjustable robust solutions of uncertain linear programs," Mathematical Programming, vol. 99, no. 2, pp. 351-376, Mar. 2004.
15. ∞-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Boston, MA: Birkhauser, 1991.
16. M. Green and D. J. N. Limebeer, Linear Robust Control. Englewood Cliffs, NJ: Prentice Hall, 1995.
17. D. J. Hill and P. J. Moylan, "Connections between finite-gain and asymptotic stability," IEEE Trans. Automat. Control, vol. AC-25, no. 5, pp. 931-936, Oct. 1980.
18. ∞ output feedback control for nonlinear systems," IEEE Trans. Automat. Control, vol. 40, no. 6, pp. 1007-1017, Jun. 1995.
19. H. K. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice Hall, 2002.
20. J. Löfberg, "Minimax Approaches to Robust Model Predictive Control," Ph.D. dissertation, Linköping University, Linköping, Sweden, Apr. 2003.
21. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge University Press, 2004.
22. P. J. Goulart, "Affine Feedback Policies for Robust Control With Constraints" Ph.D. dissertation, University of Cambridge, Cambridge, U.K., Nov. 2006 [Online]. Available: http://www-control.eng.cam.ac.uk
23. F. Blanchini, "Set invariance in control," Automatica, vol. 35, no. 1, pp. 1747-1767, Nov. 1999.
24. M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, "Applications of second-order cone programming," Linear Algebra Appl., vol. 284, no. 1-3, pp. 193-228, Nov. 1998.