Active vibration control of nonlinear flexible structures via reduction on spectral submanifolds

Cong Shen, Mingwu Li

correctmedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper derives the reduced O(ε) linear, time-varying affine system by projecting onto the B-orthonormal generalized eigenbasis and obtains the same extended LQ formulation and feedback law via Pontryagin’s principle, including the Riccati and s(t) equations and the initial/terminal conditions (see equations (28)–(29) and (41)–(45), then (59)–(66) in the PDF) . The candidate solution uses dynamic programming/HJB with a quadratic value-function ansatz to reach the identical control law and ODEs, and its projection step is consistent with the paper’s aperiodic-SSM decomposition after choosing S0(t)=0 to obtain the linear controlled surrogate (equations (16)–(20)) . Differences are methodological rather than substantive.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

A solid and carefully developed framework that leverages SSMs to separate nonlinear reduced dynamics (offline) from a tractable linear controlled surrogate (online), enabling an extended LQR design. The mathematics is correct at the stated approximation order and the overall contribution is useful to the vibration control community. Minor clarifications on specific modeling choices and notational conventions would further improve readability and rigor.