Invariance kernels of single-input planar nonlinear systems

Proceedings of the American Control Conference

Volumn , Issue , 2011, Pages 1420-1425

  Maggiore, Manfredi ^a   Rawn, Barry ^b   Lehn, Peter ^a  

^a UNIVERSITY OF TORONTO   (Canada)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL ENGINEERING;

CLOSED SET; CONNECTED SETS; EXTREMAL VECTOR FIELDS; FINITE NUMBER; MEASURABLE INPUTS; PLANAR NONLINEAR SYSTEMS; SINGLE INPUT; SPECIAL POINTS;

NONLINEAR CONTROL SYSTEMS;

EID: 80053167272     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2011.5990783     Document Type: Conference Paper

References (18)

1. J. Aubin, Viability Theory. Birkhäuser Boston, 1991.
2. H. Frankowska and M. Quincampoix, "Viability kernels of differential inclusions with constraints: algorithm and applications," Journal of Mathematical Systems, Estimation and Control, vol. 1, no. 3, pp. 371-388, 1991.
3. P. Saint-Pierre, "Approximation of the viability kernel," Applied Mathematics and Optimization, vol. 29, pp. 187-209, 1994.
4. J. Rieger, "Shadowing and the viability kernel algorithm," Applied Mathematics and Optimization, vol. 60, pp. 429-441, 2009.
5. J.-P. Aubin and A. Cellina, Differential Inclusions: Set-Valued Maps and Viability Theory. Springer, Berlin, 1984.
6. B. G. Rawn, "Ensuring safe exploitation of wind turbine kinetic energy: An invariance kernel formulation," Ph.D. dissertation, University of Toronto, 2009.
7. M. Broucke and J. Turriff, "Viability kernels for nonlinear control systems using bang controls," IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1280-1284, 2010.
8. A. Agrachev and D. Liberzon, "Lie-algebraic stability criteria for switched systems," SIAM Journal on Control and Optimization, vol. 40, pp. 253-269, 2001.
9. M. Margaliot and D. Liberzon, "Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions," Systems and Control Letters, vol. 55, pp. 8-16, 2006. (Pubitemid 41737276)
10. U. Boscain, G. Charlot, and M. Sigalotti, "Stability of planar nonlinear switched systems," Discrete and Continuous Dynamical Systems (DCDS-A), vol. 15, no. 2, pp. 415-432, 2006.
11. M. Baitman, "Controllability regions in the plane," M.M Differents. Uravn, vol. 14, no. 4, pp. 407-417, 1978.
12. N. Butenina, "Immunity zones of controlled dynamical systems,"Differential Equations, vol. 35, no. 5, pp. 634-641, 1999.
13. A. Davydov, Qualitative theory of control systems. American Mathematical Society, 1994.
14. A. Filippov, Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, 1988.
15. F. Clarke, Y. S. Ledyaev, R. Stern, and P. Wolenski, Nonsmooth Analyisis and Control Theory. Springer, 1991.
16. M. Quincampoix, "Differential inclusions and target problems," SIAM Journal on Control and Optimization, vol. 30, no. 2, pp. 324-335, 1992.
17. J. Aubin, "Viability kernels and capture basins of sets under differential inclusions," SIAM Journal of Control and Optimization, vol. 40, no. 3, pp. 853-881, 2001.
18. R. Tarjan, "Enumeration of the elementary circuits of a directed graph," SIAM Journal on Computing, vol. 2, no. 3, pp. 211-216, 1973.