Optimal control in opinion dynamics models: towards a unified framework

Ivan V. Kozitsin

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves existence via Filippov-type hypotheses and applies the Pontryagin Maximum Principle to show the optimal control maximizes a linear Hamiltonian over a simplex; when a single switching function component strictly dominates on an interval, the optimal control concentrates at a simplex vertex. The candidate solution establishes the same two pillars (existence and bang–bang structure) with more explicit verification of invariance/regularity and the Filippov conditions, and with an equivalent switching-function formula (up to an additive constant) that yields the same argmax decisions. Minor issues in the paper (a sign typo and a terse existence argument) do not affect the main results.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The core theoretical claims—existence of an optimal control under standard Filippov-type conditions and a PMP-based bang–bang characterization under strict dominance of a switching function component—are correct and align with established optimal control theory. The framework is relevant to opinion dynamics with stubborn agents and the numerical studies are informative. Minor revisions addressing a small sign typo and expanding the existence argument and switching-function discussion would strengthen the presentation.