Second-order optimality conditions and stability for optimal control problems governed by viscous Camassa-Holm equations

TL;DR

This paper extends the analysis of optimal control problems governed by viscous Camassa-Holm equations by establishing second-order optimality conditions and stability results, enhancing understanding of solution robustness.

Contribution

It introduces second-order sufficient optimality conditions and Lipschitz stability analysis for control systems governed by viscous Camassa-Holm equations.

Findings

Second-order optimality conditions established

Lipschitz stability of control system proved

Enhanced robustness understanding of control solutions

Abstract

This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form were proved for a distributed optimal control problem governed by the three-dimensional viscous Camassa-Holm equations in bounded domains with the cost functional of a quite general form and pointwise control constraints. We will establish the second-order sufficient optimality conditions as well as the Lipschitz stability results of the control system with respect to perturbations of the initial data.