Differential flatness reduces the Euler-Lagrange equation of controllable LQ problems to exponential-polynomial solutions whose stable-unstable splitting produces the exponential turnpike under stated nondegeneracy conditions.
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A flatness proof of the exponential turnpike phenomenon for linear-quadratic optimal control problems
Differential flatness reduces the Euler-Lagrange equation of controllable LQ problems to exponential-polynomial solutions whose stable-unstable splitting produces the exponential turnpike under stated nondegeneracy conditions.