Efficient computation of Robust Positively Invariant sets with linear state-feedback gain as a variable of optimization

Program and Abstract Book - 2010 7th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2010

Volumn , Issue , 2010, Pages 199-204

  Tahir, Furqan ^a  

^a COMSATS Institute of Information Technology ^*  (Pakistan)

Author keywords

Farkas lemma; Linear matrix inequalities; S procedure; Set invariance

Indexed keywords

ADDITIVE DISTURBANCE; CONTROL LAWS; CORRESPONDING STATE; EFFICIENT COMPUTATION; FARKAS LEMMA; INPUT CONSTRAINTS; INVARIANT SET; LINEAR DISCRETE-TIME SYSTEMS; LINEAR MATRIX; LINEAR PROGRAMS; NUMERICAL EXAMPLE; ONE STEP; ROBUST POSITIVELY INVARIANT SET; S-PROCEDURE; SEMIDEFINITE PROGRAMS; SET INVARIANCE; STATE CONSTRAINTS;

ALGORITHMS; AUTOMATION; CONTROL; DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; ELECTRICAL ENGINEERING; FEEDBACK; LINEAR MATRIX INEQUALITIES; OPTIMIZATION; PROCESS CONTROL; ROBUST CONTROL; STATE FEEDBACK;

COMPUTATIONAL EFFICIENCY;

EID: 78650284639     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICEEE.2010.5608613     Document Type: Conference Paper

References (21)

1. F. Blanchini, "Set invariance in control," Automatica, vol. 35, pp. 1747-1767, 1999.
2. P. O. M. Scokaert and D. Q. Mayne, "Min-max feedback model predictive control for constrained linear systems," IEEE Trans. On Automatic Control, vol. 43, pp. 1136-1142., 1998.
3. W. Langson, I. Chryssochoos, S. V. Rakovic, and D. Q. Mayne, "Robust model predictive control using tubes," Automatica, vol. 40, pp. 125-133, 2004.
4. J. D. Glover and F. C. Schweppe, "Control of linear dynamic systems with set constrained disturbances," IEEE Trans. on Automatic Control,vol. 16, pp. 411-423, 1971.
5. D. Q. Mayne and W. R. Schroeder, "Robust time-optimal control of constrained linear systems," Automatica, vol. 33, pp. 2103-2118, 1997.
6. D. P. Bertsekas and I. B. Rhodes, "On the minimax reachability of target sets and target Tubes," Automatica, vol. 7, pp. 233-247, 1971.
7. I. Kolmanovsky and E. G. Gilbert, "Theory and computation of disturbance invariant sets for discrete-time linear systems," Mathematical Problems in Engineering, vol. 4, pp. 317-367, 1998.
8. J. Löfberg, "Minimax approaches to robust model predictive control," PhD thesis, Linköping University, 2003.
9. E. Gilbert and K. Tan, "Linear systems with state and control constraints: The theory and application of maximal output admissible sets," IEEE Trans. on Automatic Control, vol. 36, pp. 1008-1020, 1991.
10. B. Pluymers, B. Rossiter, J. Suykens, and B. De Moor, "Interpolation based MPC for LPV systems using Polyhedral invariant sets," in Proc. of the American Control Conf., pp. 810-815, 2005.
11. S. V. Rakovic, E. C. Kerrigan, K. I. Kouramas, and D. Q. Mayne, "Invariant approximations of the minimal robust positively invariant set," IEEE Trans. on Automatic Control, vol. 50, pp. 406-410, 2005.
12. C.-J. Ong, and E. G. Gilbert, "The minimal disturbance invariant set: Outer approximations via its partial sums," Automatica, vol. 42, pp. 1563-1568, 2006.
13. S. V. Rakovic, and K. I. Kouramas, "The minimal robust positively invariant set for linear discrete time systems: Approximation methods and control applications," in Proc. of the 45th IEEE Conf. on Decision and Control, San Diego, USA, 2006.
14. H. Benlaoukli, S. Olaru, S. Marinkovic and P. Boucher, "Invariant set constructions for feasible reference tracking," in Proc. of the IEEE International Conf. on Control and Automation, Christchurch, New Zeland, 2009.
15. U. T. Jonsson, "A Lecture on the S-procedure," Lecture notes, Division of Optimization and Systems Theory, Royal Institute of Technology, Stockholm, Sweden, 2006.
16. K. Anstreicher and H. Wolkowicz, "On lagrangian relaxation of quadratic matrix constraints," SIAM Journal on Matrix Analysis and Applications, vol. 22, no. 1, pp. 41-55, 2000.
17. T. Fujie and M. Kojima, "Semidefinite programming relaxation for nonconvex quadratic programs," Global Optimization, vol. 10, pp. 367-380, 1997.
18. H. Wolkowicz, R. Saigal, and L. Vandenberghe, Handbook of Semidefinite Programming: Theory, Algorithms and Applications, Kluwer Academic, 2000.
19. U. Malik, I. M. Jaimoukha, G. D. Halikias, and S. K. Gungah, On the gap between the quadratic integer programming problem and its semidefinite relaxation. Mathematical Programming, vol. 107, pp. 505-515, 2006.
20. C. Fortin and H. Wolkowicz, " The trust region subproblem and semidefnite programming," Optimization Methods and Software, vol. 19, no. 1, pp. 41-67, 2004.
21. J. J. Moré, "Generalization of the trust region problem," Optimization Methods and Software, vol. 2, pp. 189-209, 1993.