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

✍ Scribed by E. Fridman

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
127 KB
Volume
40
Category
Article
ISSN
0167-6911

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✦ Synopsis

We study the inÿnite horizon nonlinear quadratic optimal control problem for a singularly perturbed system, which is nonlinear in both, the slow and the fast variables. It is known that the optimal controller for such problem can be designed by ÿnding a special invariant manifold of the corresponding Hamiltonian system. We obtain exact slow-fast decomposition of the Hamiltonian system and of the special invariant manifold into the slow and the fast ones. On the basis of this decomposition we construct high-order asymptotic approximations of the optimal state-feedback and optimal trajectory.

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