Higher order necessary conditions for optimal controls not ranging in the interior

2025/05/01 by Angrisani, Francesca, Rampazzo, Franco
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2505.00790

Abstract

Goh's and Legendre-Clebsch necessary conditions for optimal controls of affine-control systems are usually established under the hypothesis that the minimizing control lies in the interior of the control set U. In this paper we investigate the possibility of establishing Goh's and Legendre-Clebsch necessary conditions without this assumption, so that even control sets with empty interiors or optimal controls touching the boundary of U can be taken into consideration.

Citations

• Goh and Legendre-Clebsh conditions for nonsmooth control systems
• Goh conditions for minima of nonsmooth problems with unbounded controls
• Second-order sensitivity relations and regularity of the value function\n for Mayer's problem in optimal control
• Pontryagin Maximum Principle for finite dimensional nonlinear optimal control problems on time scales

Related

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• Goh conditions for minima of nonsmooth problems with unbounded controls
• Singular extremals of optimal control problems with L¹ cost
• Second-Order Necessary/Sufficient Conditions for Optimal Control Problems in the Absence of Linear Structure
• Necessary conditions for optimal control problems with sweeping systems and end point constraints