Quadratic order conditions for bang-singular extremals
Maria Soledad Aronna (CIFASIS CONICET, INRIA Saclay - Ile de France,, CMAP, CIFASIS), J. Frederic Bonnans (INRIA Saclay - Ile de France, CMAP),, Andrei V. Dmitruk (CEMI, Lomonosov Moscow State University), Pablo Lotito, (PLADEMA CONICET)
TL;DR
This paper develops second order necessary and sufficient optimality conditions for control systems with control constraints and state constraints, advancing the theoretical understanding of bang-singular extremals.
Contribution
It introduces second order necessary conditions and a sufficient condition for scalar controls in affine control systems with constraints.
Findings
Second order necessary optimality conditions derived.
A second order sufficient condition established for scalar control cases.
Enhanced theoretical framework for bang-singular extremals.
Abstract
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case.
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