Intersection-based piecewise affine approximation of nonlinear systems

2013 21st Mediterranean Conference on Control and Automation, MED 2013 - Conference Proceedings

Volumn , Issue , 2013, Pages 640-645

  Zavieh, Amin ^a   Rodrigues, Luis ^a  

^a Dept of Electrical and Computer Engineering   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ERRORS; APPROXIMATION METHODS; CONTINUOUS FUNCTIONS; EXTENSION METHODS; MAXIMUM ERROR; NUMERICAL OPTIMIZATIONS; PIECEWISE AFFINE APPROXIMATION; PIECEWISE AFFINES;

APPROXIMATION ALGORITHMS; FUNCTIONS; NONLINEAR SYSTEMS; OPTIMIZATION;

LINEARIZATION;

EID: 84885236775     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/MED.2013.6608790     Document Type: Conference Paper

References (27)

1. Mikael Johansson. Piecewise Linear Control Systems. Springer-Verlag, Berlin, first edition, 2003.
2. L. Rodrigues and J.P. How. Synthesis of piecewise-affine controllers for stabilization of nonlinear systems. Proceedings of the 42nd IEEE Conference on Decision and Control, 3:2071-2076, 2003.
3. L. Rodrigues and S. Boyd. Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization. Systems & Control Letters, 54:835-853, 2005.
4. S. Casselman and L. Rodrigues. Piecewise affine modeling of a micro air vehicle using voronoi partitions. In Proceedings of the European Control Conference, pages 3857-3862, 2009.
5. A. Cantoni. Optimal curve fitting with piecewise linear functions. IEEE Transactions on Computers, C-20:59-67, January 1971.
6. I. Tomek. Two algorithms for piecewise-linear continuous approximation of functions of one variable. IEEE Transactions on Computers, C-24:445-448, April 1974.
7. P. Julian, A. Desages, and O. Agamennoni. High-level canonical piecewise linear representation using a simplicial partition. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46:1057-7122, April 1999.
8. Richard E. Groff, Pramod P. Khargonekar, and Daniel E. Koditschek. A local convergence proof for the MINVAR algorithm for computing continuous piecewise linear approximations. SIAM Journal of Numerical Analysis, 41(3):983-1007, 2003.
9. S. Azuma, J. Imura, and T. Sugie. Lebesgue piecewise affine approximation of nonlinear systems. Nonlinear Analysis: Hybrid Systems, 4(1):92-102, 2010
10. Marco Storace and Oscar De Feo. Piecewise-linear approximation of nonlinear dynamical systems. IEEE Transactions on Circuits and Systems, Vol. 51(No. 4):830-842, 2004
11. Jorge M. Gonçalves, Alexandre Megretski, and Munther A. Dahleh. Global analysis of piecewise linear systems using impact maps and surface lyapunov functions. IEEE Transactions on Automatic Control, Vol. 48(No. 12):2089-2106, 2003
12. E. Asarin, T. Dang, and A. Girard. Hybrid Systems: Computation and Control, pages 20-35. Springer, 2003
13. Gang Feng. Controller design and analysis of uncertain piecewiselinear systems. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, Vol. 49(No. 2):224-232, 2002
14. Luis Rodrigues and Jonathan P. How. Automated Control Design for a Piecewise-Affine Approximation of a Class of Nonlinear Systems. In Proceedings of the American Control Conference, pages 3189-3194, 2001
15. Wei Yue, Luis Rodrigues, and Brandon Gordon. Piecewise-affine control of a three DOF helicopter. In Proceedings of the 2006 American Control Conference, pages 3924-3929, 2006
16. Daniele Corona and Bart De Schutter. Adaptive cruise control for a SMART car: A comparison benchmark for MPC-PWA control methods. IEEE Transactions on Control Systems Technology, Vol. 16(Number 2):365-372, 2008
17. G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari. A clustering technique for the identification of piecewise affine systems. Automatica, 39(2):205-217, 2003
18. A. Bemporad and M. Morari. Control of systems integrating logic, dynamics, and constraints. AUTOMATICA-OXFORD-, 35:407-428, 1999
19. C. Tomlin, I. Mitchell, and R. Ghosh. Safety verification of conflict resolution manoeuvres. Intelligent Transportation Systems, IEEE Transactions on, 2(2):110-120, 2001
20. R. Ghosh, A. Tiwari, and C. Tomlin. Automated symbolic reachability analysis; with application to delta-notch signaling automata. Hybrid Systems: Computation and Control, pages 233-248, 2003
21. S.I. Azuma and J.I. Imura. Polynomial-time probabilistic controllability analysis of discrete-time piecewise affine systems. Automatic Control, IEEE Transactions on, 52(11):2029-2046, 2007
22. S. Azuma and J. Imura. Polynomial-time probabilistic observability analysis of sampled-data piecewise affine systems. In Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC\'05. 44th IEEE Conference on, pages 6644-6649. IEEE, 2005
23. Behzad Samadi and Luis Rodrigues. Extension of local linear controllers to global piecewise affine controllers for uncertain nonlinear systems. International Journal of Systems Science, 39(9):867-879, 2008
24. A. Zavieh. Pseudo Euler-Lagrange and Piecewise Affine Control Applied to Surge and Stall in Axial Compressors. Master's thesis, Dept. of Electrical and Computer Engineering, Concordia University, Fabruary 2013
25. H.L. Royden. Real Analysis. MACMILLAN, second edition, 1968
26. S. Casselman and L. Rodrigues. A new methodology for piecewise affine models using voronoi partitions. In Proc. 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pages 3920-3925, 2009
27. S. Afkhami and H. Alighanbari. Nonlinear control design of an airfoil with active flutter suppression in the presence of disturbance. IET Control Theory Appl., 1(6):1638-1649, November 2007