Exact slow-fast decomposition of the nonlinear singularly perturbed optimal control problem

Systems and Control Letters

Volumn 40, Issue 2, 2000, Pages 121-131

  Fridman, E ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Hamiltonian systems; Invariant manifolds; Nonlinear optimal control; Order reduction; Singular perturbations

Indexed keywords

EID: 0346736775     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(00)00008-6     Document Type: Article

References (12)

1. C. Byrnes, On the Riccati partial differential equation for nonlinear Bolza and Lagrange problems, J. Math. Systems, Estimation Control 8 (1998) 1-54.
2. J. Chow, P. Kokotovic, Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems, SIAM J. Control Optim. 16 (1978) 756-770.
3. ∞ control of linear singularly perturbed systems, IEEE Trans. Automat. Control AC-41 (1996) 236-240.
4. E. Fridman, Exact slow-fast decomposition of a class of nonlinear singularly perturbed optimal control problems via invariant manifolds, Internat. J. Control 72 (1999) 1609-1618.
5. V. Kecman, S. Bigulac, Z. Gajic, Eigenvector approach for order reduction of singularly perturbed linear-quadratic optimal control problems, Automatica 35 (1999) 151-158.
6. A. Kelley, The stable, center-stable, center, center-unstable, and unstable manifolds, J. Differential Equations 3 (1967) 546-570.
7. P. Kokotovic, H. Khalil, J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, New York, 1986.
8. D. Lukes, Optimal regulation of nonlinear systems, SIAM J. Control 7 (1969) 75-100.
9. R. O'Malley, Introduction to Singular Perturbations, Academic Press, New York, 1974.
10. V. Sobolev, Integral manifolds and decomposition of singularly perturbed systems, Systems & Control Letters 4 (1984) 169-179.
11. W. Su, Z. Gajic, X. Shen, The exact slow-fast decomposition of the algebraic Riccati equation of singularly perturbed systems, IEEE Trans. Automat. Control AC-37 (1992) 1456-1459.
12. Y. Wang, S. Shi, Z. Zhang, A descriptor-system approach to singular perturbation of linear regulators, IEEE Trans. Automat. Control 33 (1988) 370-373.