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Malanowski, K.; Maurer, H.; Pickenhain, S.

Second-order sufficient conditions for state-constrained optimal control problems. (English) Zbl 1059.49027

J. Optimization Theory Appl. 123, No. 3, 595-617 (2004).
Summary: Second-order sufficient optimality conditions (SSC) are derived for an optimal control problem subject to mixed control-state and pure state constraints of order one. The proof is based on a Hamilton-Jacobi inequality and it exploits the regularity of the control function as well as the associated Lagrange multipliers. The obtained SSC involve the strict Legendre-Clebsch condition and the solvability of an auxiliary Riccati equation. They are weakened by taking into account the strongly active constraints.

Cited in 20 Documents

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
49L99 Hamilton-Jacobi theories

Keywords:

nonlinear optimal control; mixed control-state constraints; first-order state constraints; second-order sufficient optimality conditions; constraint qualifications; Legendre-Clebsch condition; solvability of a Riccati equation; Hamilton-Jacobi inequality

Software:

BNDSCO
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Full Text: DOI

References:

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