Numerical Optimal Control with Periodicity Constraints in the Presence of Invariants

Gros, Sebastien and Zanon, Mario Numerical Optimal Control with Periodicity Constraints in the Presence of Invariants. IEEE Transactions on Automatic Control. p. 1. ISSN 0018-9286 (In Press) (2017)

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Abstract

Periodic optimal control problems (POCPs) based on dynamic models holding invariants are often problematic to treat using standard numerical methods. The difficulty stems from a failure of standard constraint qualifications and typically hinders the convergence of the numerical solver, or even defeats it. Optimisation problems having weak constraint qualifications can be treated using dedicated solvers, at the price of a more involved algorithmic. In this paper, we analyse the constraint qualification of POCPs holding invariants, and propose three simple and computationally inexpensive modifications of the formulation that allow for a recovery of Linear Independence Constraint Qualification (LICQ), while not affecting the Second-Order Sufficient Conditions (SOSC) for optimality. Hence, the resulting POCP can be tackled via standard solvers, without special treatment. The application of these approaches is detailed for the case of POCPs holding index-reduced Differential-Algebraic Equations and representations of the SO(3) Lie group.

Item Type:	Article
Identification Number:	https://doi.org/10.1109/TAC.2017.2772039
Subjects:	T Technology > T Technology (General)
Research Area:	Computer Science and Applications
Depositing User:	Mario Zanon
Date Deposited:	09 Mar 2018 14:07
Last Modified:	09 Mar 2018 14:07
URI:	http://eprints.imtlucca.it/id/eprint/4001

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