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Normality and Nondegeneracy for Optimal Control Problems with State Constraints

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Abstract

In this paper, we investigate normal and nondegenerate forms of the maximum principle for optimal control problems with state constraints. We propose new constraint qualifications guaranteeing nondegeneracy and normality that have to be checked on smaller sets of points of an optimal trajectory than those in known sufficient conditions. In fact, the constraint qualifications proposed impose the existence of an inward pointing velocity just on the instants of time for which the optimal trajectory has an outward pointing velocity.

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Acknowledgments

The partial supports of projects FP7-ITN-264735-SADCO “Sensitivity Analysis for Deterministic Controller Design” and FCT/FEDER Project PTDC/EEA-CRO/116014/2009 “Optimal Control in Constrained and Hybrid Nonlinear Systems”, PTDC/EEI-AUT/1450/2012 “Optimal Control: Health, Energy and Robotics Applications” are gratefully acknowledged.

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Authors and Affiliations

  1. SYSTEC-ISR, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto, Portugal

    Fernando A. C. C. Fontes

  2. CNRS, IMJ-PRG, UMR 7586, Sorbonne Universits, UPMC Univ Paris 06, Univ Paris Diderot, Sorbonne Paris Cité, Case 247, 4 Place Jussieu, 75252, Paris, France

    Hélène Frankowska

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  1. Fernando A. C. C. Fontes
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  2. Hélène Frankowska
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Correspondence to Fernando A. C. C. Fontes.

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Fontes, F.A.C.C., Frankowska, H. Normality and Nondegeneracy for Optimal Control Problems with State Constraints. J Optim Theory Appl 166, 115–136 (2015). https://doi.org/10.1007/s10957-015-0704-1

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