An interior penalty method for optimal control problems with state and input constraints of nonlinear systems.

*(English)*Zbl 1336.49038Summary: This paper exposes a methodology to solve state and input constrained optimal control problems for nonlinear systems. In the presented “interior penalty” approach, constraints are penalized in a way that guarantees the strict interiority of the approaching solutions. This property allows one to invoke simple (without constraints) stationarity conditions to characterize the unknowns. A constructive choice for the penalty functions is exhibited. The property of interiority is established, and practical guidelines for implementation are given. A numerical benchmark example is given for illustration.

##### MSC:

49M30 | Other numerical methods in calculus of variations (MSC2010) |

90C51 | Interior-point methods |

93C10 | Nonlinear systems in control theory |

93C35 | Multivariable systems, multidimensional control systems |

##### Keywords:

optimal control; nonlinear systems; state constraints; input constraints; interior penalty method
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\textit{P. Malisani} et al., Optim. Control Appl. Methods 37, No. 1, 3--33 (2016; Zbl 1336.49038)

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