@misc{Malanowski_Kazimierz._Autor_Second_2003,
 author={Malanowski, Kazimierz. Autor},
 copyright={Creative Commons Attribution BY 4.0 license},
 address={Warszawa},
 journal={Raport Badawczy = Research Report},
 howpublished={online},
 year={2003},
 publisher={Instytut Badań Systemowych. Polska Akademia Nauk},
 publisher={Systems Research Institute. Polish Academy of Sciences},
 language={eng},
 abstract={Second order sufficient optimality conditions (SSC) are derived, for an optimal control problem subject to pure state constraints of order one. The proof is based on a Hamilton-Jacobi inequality and it exploits regularity of the control function, as well as the associated Lagrange multipliers. The obtained SSC involve Legendre-Clebsch conditions and solvability of an auxiliary Riccati equation. The latter condition is weakened by taking into account the strongly active constraints.},
 type={Text},
 title={Second order sufficient conditions for optimal control subject to first order state constraints},
 keywords={Nonlinear optimal control, First order state constraints, Second order sufficient optimality conditions, Constraint qualifications, Legendre-clebsch condition, Solvability of a riccati equation, Sterowanie optymalne nielinowe},
}