Optimal control of differential inclusions on manifolds

Robert J. Kipka; Yuri S. Ledyaev

doi:10.3934/dcds.2015.35.4455

Article Contents

2015, Volume 35, Issue 9: 4455-4475. Doi: 10.3934/dcds.2015.35.4455

This issue Previous Article Dynamic programming using radial basis functions Next Article Uniform convergence of the POD method and applications to optimal control

Optimal control of differential inclusions on manifolds

Robert J. Kipka^1, and
Yuri S. Ledyaev^2,

1.
Department of Mathematics and Statistics, Queen's University, Kingston, ON, K7L 3N6
2.
Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008-5248

Received: April 2014

Revised: October 2014

Published: May 2017

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Abstract

Dynamic optimization problems for differential inclusions on manifolds are considered. A mathematical framework for derivation of optimality conditions for generalized dynamical systems is proposed. We obtain optimality conditions in form of generalized Euler-Lagrange relations and in form of partially convexified Hamiltonian inclusions by using metric regularity of terminal and dynamic constraints.

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Mathematics Subject Classification: Primary: 49K21, 49K27; Secondary: 34A60.

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