Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems

K. Malanowski, H. Maurer and S. Pickenhain
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K. Malanowski: Polish Academy of Sciences
H. Maurer: Westfälische Wilhelms-Universität
S. Pickenhain: Westfälische Wilhelms-Universität

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 3, No 8, 595-617

Abstract: Abstract 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.

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 (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-004-5725-0

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