On efficient computation of low-complexity controlled invariant sets for uncertain linear systems

International Journal of Control

Volumn 83, Issue 7, 2010, Pages 1339-1346

  Blanco, Toni Barjas ^a   Cannon, Mark ^b   De Moor, Bart ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

constrained control; optimisation; polytopic invariant sets

Indexed keywords

CONSTRAINED CONTROLS; CONSTRAINED PROBLEM; CONVEX PROGRAMS; EFFICIENT COMPUTATION; HIGH ORDER SYSTEMS; INVARIANT SET; ITERATIVE SEQUENCES; LINEAR FEEDBACK; LOW-COMPLEXITY; OPTIMISATIONS; POLYTOPES; POLYTOPIC UNCERTAINTIES; SEMIDEFINITE PROGRAMS; UNCERTAIN LINEAR SYSTEM;

OPTIMIZATION;

LINEAR SYSTEMS;

EID: 77954077295     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207171003692662     Document Type: Article

References (15)

1. Agudelo, M., Espinosa, J., and De Moor, B. (2006), 'Application of POD and Predictive Control Techniques to the Control of the Temperature Profile of an One-dimensional Bar', in Proceedings of the XII Latin-American Congress on Automatic Control (CLCA 2006), pp. 127-132.
2. Benzaouia, A., and Burgat, C. (1988), 'Regulator Problem for Linear Discrete-time Systems with Nonsymmetrical Constrained Control', International Journal of Control, 48, 2441-2451. (Pubitemid 18633112)
3. Berman, A., and Plemmons, R. (1994), Nonnegative Matrices in the Mathematical Sciences, Philadelphia: SIAM.
4. Bitsoris, G. (1988), 'On the Positive Invariance of Polyhedral Sets for Discrete-time Systems', Systems and Control Letters, 11, 1487-1494. (Pubitemid 18632183)
5. Blanchini, F. (1991), 'Constrained Control for Uncertain Linear Systems', Journal of Optimization Theory and Applications, 71, 465-484.
6. Blanchini, F. (1999), 'Set Invariance in Control', Automatica, 35, 1747-1767. (Pubitemid 32078089)
7. Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994), Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM.
8. Cannon, M., Deshmukh, V., and Kouvaritakis, B. (2003), 'Nonlinear Model Predictive Control with Polytopic Invariant Sets', Automatica, 39, 1478-1494.
9. Gilbert, E., and Tan, K. (1991), 'Linear Systems with State and Control Constraints: The Theory and Application of Maximal Output Admissible Sets', IEEE Transactions on Automatic Control, 36, 1008-1020. (Pubitemid 21689717)
10. Hennet, J.-C., and Beziat, J.-P. (1991), 'A Class of Invariant Regulators for the Discrete-time Linear Constrained Regulation Problem', Automatica, 27, 549-554. (Pubitemid 21651850)
11. Kothare, M., Balakrishnan, V., and Morari, M. (1996), 'Robust Constrained Model Predictive Control using Linear Matrix Inequalities', Automatica, 32, 1361-1379. (Pubitemid 126365465)
12. Lee, Y., Cannon, M., and Kouvaritakis, B. (2005), 'Extended Invariance and Its Use in Model Predictive Control', Automatica, 41, 2163-2169. (Pubitemid 41525677)
13. Lee, Y., and Kouvaritakis, B. (2000), 'Robust Receding Horizon Predictive Control for Systems with Uncertain Dynamics and Input Saturation', Automatica, 36, 1497-1504. (Pubitemid 32528800)
14. Pluymers, B., Rossiter, J., Suykens, J., and De Moor, B. (2005a), 'Interpolation Based MPC for LPV Systems using Polyhedral Invariant Sets', in Proceedings of the American Control Conference, pp. 810-815. (Pubitemid 41189216)
15. Pluymers, B., Rossiter, J., Suykens, J., and De Moor, B. (2005b), 'The Efficient Computation of Polyhedral Invariant Sets for Linear Systems with Polytopic Uncertainty', in Proceedings of the American Control Conference, pp. 804-809. (Pubitemid 41189215)