# Inversion in indirect optimal control: constrained and unconstrained cases

Authors: F. Chaplais, N. Petit, 46th IEEE Conference on Decision and Control, December 2007, New Orleans, pp. 683-689 DOI: 10.1109/CDC.2007.4434074
This paper focuses on using non linear inversion in optimal control problems. This technique allows us to rewrite the stationarity conditions derived from the calculus of variations under a higher order form with a reduced number of variables. After a brief tutorial overview of the multi- input multi-output cases for which the cost functions have a positive definite Hessian with respect to control variables, we address the case of linear systems with a control affine cost to be minimized under input constraints. This is the main contribution of this paper. We study the switching function between singular and regular arcs and explain how higher order stationarity conditions can be obtained. An example from the literature (energy optimal trajectory for a car) is addressed.
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BibTeX:
@Proceedings{,
author = {F. Chaplais, N. Petit},
editor = {},
title = {Inversion in indirect optimal control: constrained and unconstrained cases},
booktitle = {46th IEEE Conference on Decision and Control},
volume = {},
publisher = {},
address = {New Orleans},
pages = {683-689},
year = {2007},
abstract = {This paper focuses on using non linear inversion in optimal control problems. This technique allows us to rewrite the stationarity conditions derived from the calculus of variations under a higher order form with a reduced number of variables. After a brief tutorial overview of the multi- input multi-output cases for which the cost functions have a positive definite Hessian with respect to control variables, we address the case of linear systems with a control affine cost to be minimized under input constraints. This is the main contribution of this paper. We study the switching function between singular and regular arcs and explain how higher order stationarity conditions can be obtained. An example from the literature (energy optimal trajectory for a car) is addressed.},
keywords = {}}