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A HIGHER-ORDER MAXIMUM PRINCIPLE FOR IMPULSIVE OPTIMAL CONTROL PROBLEMS.

Authors :
ARONNA, M. SOLEDAD
MOTTA, MONICA
RAMPAZZO, FRANCO
Source :
SIAM Journal on Control & Optimization. 2020, Vol. 58 Issue 2, p814-844. 31p.
Publication Year :
2020

Abstract

We consider a nonlinear system, affine with respect to an unbounded control u which is allowed to range in a closed cone. With this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to u. This lack of coercivity gives the problem an impulsive character, meaning that minimizing sequences of trajectories happen to converge towards discontinuous paths. As is known, a distributional approach does not make sense in such a nonlinear setting, where, instead, a suitable embedding in the graph space is needed. We provide higher-order necessary optimality conditions for properly defined impulsive minima in the form of equalities and inequalities involving iterated Lie brackets of the dynamical vector fields. These conditions are derived under very weak regularity assumptions and without any constant rank conditions. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
03630129
Volume :
58
Issue :
2
Database :
Academic Search Index
Journal :
SIAM Journal on Control & Optimization
Publication Type :
Academic Journal
Accession number :
148461848
Full Text :
https://doi.org/10.1137/19M1273785