Abstract

We consider state constrained optimal control problems in which the cost to minimize comprises both integral and end-point terms, establishing normality of the generalized Euler-Lagrange condition. Simple examples illustrate that the validity of the Euler-Lagrange condition (and related necessary conditions), in normal form, depends crucially on the interplay between velocity sets, the left end-point constraint set and the state constraint set. We show that this is actually a common feature for general state constrained optimal control problems, in which the state constraint is represented by closed convex sets and the left end-point constraint is a closed set. In these circumstances classical constraint qualifications involving the state constraints and the velocity sets cannot be used alone to guarantee normality of the necessary conditions. A key feature of this paper is to prove that the additional information involving tangent vectors to the left end-point and the state constraint sets can be used to establish normality.

Author information

Contact details are reproduced from the original publication and may be historical.

Piernicola Bettiol

Laboratoire de Mathématiques, Université de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, 29200 Brest, France

piernicola.bettiol@univ-brest.fr

Nathalie Khalil

Laboratoire de Mathématiques, Université de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, 29200 Brest, France

nathalie.khalil@univ-brest.fr

Richard B. Vinter

Dept. of Electrical and Electronic Engineering, Imperial College, Exhibition Road, London SW7 2BT, England

r.vinter@imperial.ac.uk

Keywords

  • Optimal Control
  • Necessary Conditions
  • Differential Inclusions
  • State Constraints

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Suggested citation

P. Bettiol, N. Khalil, R. B. Vinter. “Normality of Generalized Euler-Lagrange Conditions for State Constrained Optimal Control Problems.” Journal of Convex Analysis 23 (2016), No. 1, 291–311. https://doi.org/10.68381/jca23011

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Published by Heldermann Verlag, 2016. Rights now held by Banach Press.