Two independent control-theory historians trace optimal control's mathematical root to Lagrange and Hamilton, not Nyquist and Bode

control-theorynyquistbodeoptimal-controllagrangehamiltonpontryaginhistory-of-technologycalculus-of-variations

Stuart Bennett — a historian of control engineering (University of Sheffield) — writes in "A Brief History of Automatic Control" (IEEE Control Systems Magazine, June 1996, DOI 10.1109/37.506394) that performance-index optimization problems have "an obvious and strong analogy with the classical variational formulations of analytical mechanics given by Lagrange and Hamilton," and credits Lev Pontryagin's 1956 maximum principle as "the generalization of Hamilton's approach to geometric optics" — a lineage running through 19th-century mechanics, not through the 1930s Bell Labs frequency-response tradition.

Independently, Frank L. Lewis (University of Texas at Arlington) makes the same root explicit in Chapter 1 of Applied Optimal Control and Estimation (Prentice-Hall, 1992), reprinted on his own institutional site: "With the advent of the space age, controls design in the United States turned away from the frequency-domain techniques of classical control theory and back to the differential equation techniques of the late 1800's... It should be realized that the work of Lagrange and Hamilton makes it straightforward to write nonlinear equations of motion for many dynamical systems." Lewis frames the 1957–1960 transition explicitly as a return past classical control to an earlier tradition, not an extension of it.

Both historians, writing separately, name the same specific mathematical ancestor (Lagrange–Hamilton calculus of variations) for the lineage the vault's claim-nyquist-bode-classical-control-to-optimal-control-bridge had proposed running through Nyquist and Bode instead. Neither states that Pontryagin, Bellman, Kelley, or Bryson cited or drew on Nyquist or Bode specifically — the absence is not merely unstated, it is the space their own accounts of the field's genealogy do not pass through. See claim-kelley-1960-reference-list-cites-no-nyquist-or-bode for the companion primary-source check.