Control of affine nonlinear systems with nilpotent structure in singular problems

Journal of Optimization Theory and Applications

Volumn 124, Issue 2, 2005, Pages 455-466

  Popescu, M ^a  

^a INSTITUTE OF MATHEMATICAL STATISTICS AND APPLIED MATHEMATICS   (Romania)

Author keywords

Affine nonlinear systems; Lie algebras; Nilpotent operators; Singular and nonsingular functionals; Vector fields; algorithm

Indexed keywords

NONLINEAR SYSTEMS; PROBLEM SOLVING;

AFFINE NONLINEAR SYSTEMS; FUNCTIONALS; LIE ALGEBRA; NILPOTENT; NILPOTENT OPERATORS; NONSINGULAR; SINGULAR AND NONSINGULAR FUNCTIONALS; SINGULAR PROBLEM; VECTOR FIELDS; Ε-ALGORITHM;

ALGEBRA;

EID: 21244456945     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-004-0945-x     Document Type: Article

References (11)

1. POPESCU, M., Singular Optimal Control for Dynamic Systems, Editura Academiei, Bucharest, Romania, 2002 (in Romanian).
2. ZUBOV, V., Théorie de la Commande, Edition Mir, Moscow, Russia, 1978 (in French).
3. BOURDACHE-SIGUERDIDJANE, H., and FLIESS, M., Optimal Feedback Control of Nonlinear Systems, Automatica, Vol. 23, No. 3, pp. 365-372, 1987.
4. BOURDACHE-SIGUERDIDJANE, H., On Application of a New Method for Computing Optimal Nonlinear Feedback Controls, Optimal Control Applications and Methods, Vol. 8, pp. 397-409, 1987.
5. BANKS, S. P., and YEW, M. K., On the Optimal Control of a Linear System and Its Relation to Lie Algebras, International Journal of Control, Vol. 43, No. 3, pp. 981-900, 1986.
6. PELLETIER, F., and POPESCU, M., Contrôl Optimal pour un Système Bilinéaire et un Coût Quadratique en Dimension Infinite, UMR 51227, CNRS, Université de Savoie, France, 2002.
7. SUSSMAN, H. J., Lie Brackets, Real Analiticity, and Geometric Control in Differential Geometric Control Theory, Progress in Mathematics, Edited by R. W. Brackett, R. S. Millman, and H. J. Sussman, Birkhauser, Boston, Massachusetts, Vol. 27, pp. 1-116, 1983.
8. LIU, H. S., YUAN, K., and LIN, W. S., On Minimum-Fuel Control of Affine Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. 34, No. 7, pp. 767-770, 1989.
9. BRESSAN, A., Local Asymptotic Approximation of Nonlinear Control Systems, International Journal of Control, Vol. 41, No. 5, pp. 1331-1336, 1985.
10. HERMES, H., Nilpotent Approximation of Control Systems and Distributions, SIAM Journal on Control and Optimization, Vol. 24, No. 4, pp. 731-736, 1986.
11. JACOBSON, D. H., and MAYNE, D. Q., Differential Dynamic Programming, Elsevier, New York, NY, 1970.