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**The control parameterization method for nonlinear optimal control: a survey.**
*(English)*
Zbl 1276.49025

Summary: The control parameterization method is a popular numerical technique for solving optimal control problems. The main idea of control parameterization is to discretize the control space by approximating the control function by a linear combination of basis functions. Under this approximation scheme, the optimal control problem is reduced to an approximate nonlinear optimization problem with a finite number of decision variables. This approximate problem can then be solved using nonlinear programming techniques. The aim of this paper is to introduce the fundamentals of the control parameterization method and survey its various applications to non-standard optimal control problems. Topics discussed include gradient computation, numerical convergence, variable switching times, and methods for handling state constraints. We conclude the paper with some suggestions for future research.

### MSC:

49M37 | Numerical methods based on nonlinear programming |

65K10 | Numerical optimization and variational techniques |

65P99 | Numerical problems in dynamical systems |

90C30 | Nonlinear programming |

93C15 | Control/observation systems governed by ordinary differential equations |

### Keywords:

optimal control; control parameterization; switching times; time-scaling transformation; state constraints
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\textit{Q. Lin} et al., J. Ind. Manag. Optim. 10, No. 1, 275--309 (2014; Zbl 1276.49025)

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