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Inversion in indirect optimal control: constrained and unconstrained cases

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.
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Contributor : François Chaplais <>
Submitted on : Monday, July 12, 2010 - 10:35:12 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM
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François Chaplais, Nicolas Petit. Inversion in indirect optimal control: constrained and unconstrained cases. 46th IEEE Conference on Decision and Control, Dec 2007, New Orleans, United States. pp.683-689, ⟨10.1109/CDC.2007.4434074⟩. ⟨hal-00501874⟩

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