ABSTRACT
This paper investigates the turnpike phenomenon for optimal control problems governed by weakly damped beam networks with spectral gaps, demonstrating non-polynomial decay rates for optimal trajectories and controls.
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Key findings
Establishes a framework for analyzing turnpike properties with non-polynomial decay rates.
Proves logarithmic and sub-polynomial turnpike theorems for beam networks with localized damping.
Derives sharp resolvent estimates characterizing the relationship between spectral properties and decay rates.
Shows that non-polynomial rates are optimal under natural geometric conditions.
Limitations & open questions
Further research needed for broader classes of PDE systems and network topologies.