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Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems |
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| Authors: | K Malanowski H Maurer S Pickenhain |
| Institution: | (1) Systems Research Institute, Polish Academy of Sciences, Poland;(2) Institut für Numerische Mathematik, Westfälische Wilhelms-Universität, Germany |
| 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 |
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