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

49K15 Optimality conditions for problems involving ordinary differential equations
49L99 Hamilton-Jacobi theories
Full Text: DOI
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