TURNPIKE CONTROL AND STATIC FINITE-PARAMETER SHAPE DESIGN FOR LINEAR ELASTODYNAMICS: A CONDITIONAL ANALYTICAL FRAMEWORK

Gugat M, Sokołowski J (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Evolution Equations and Control Theory American Institute of Mathematical Sciences (AIMS)

Book Volume: 26

Pages Range: 66-95

DOI: 10.3934/eect.2026096

Abstract

The paper separates fixed-shape optimal control, static finite-parameter design, and design dynamics for geometrically linear elastodynamics. For a fixed domain and a bounded distributed control operator, a horizon-uniform feasible stabilizing competitor yields comparison-based integral and measure turnpikes; surjective bounded actuation is one sufficient mechanism and gives an explicit exponentially damped competitor. An exact endpoint identity distinguishes the compensated energy-tracking functional from the original free-terminal functional. On finite-parameter shape families, all equations are transported to fixed reference spaces, the form and pivot operators are typed separately, and the derivatives of the transformed mass, stiffness, surface Jacobian, and traction operator are derived. The resulting general-observation value jC and energy value jE are continuously Fréchet differentiable static design objectives. Only jE is related here to long-horizon dynamic values: the compensated normalized value converges at order T−1 under a uniform right-inverse hypothesis, whereas the original free-terminal value requires an additional endpoint-layer bound. A full-domain acceleration example verifies the uniform right-inverse hypothesis on a compact shape family; localized body-force actuation is generally not covered. Boundary traction is treated through an admissible unbounded-input framework and a conditional matched-feedback criterion. The differentiated long-horizon design reduction and concrete Lamé boundary observability remain explicit assumptions rather than conclusions.

Authors with CRIS profile

Martin Gugat Naturwissenschaftliche Fakultät

Involved external institutions

Université de Lorraine FR France (FR)

How to cite

APA:

Gugat, M., & Sokołowski, J. (2026). TURNPIKE CONTROL AND STATIC FINITE-PARAMETER SHAPE DESIGN FOR LINEAR ELASTODYNAMICS: A CONDITIONAL ANALYTICAL FRAMEWORK. Evolution Equations and Control Theory, 26, 66-95. https://doi.org/10.3934/eect.2026096

MLA:

Gugat, Martin, and Jan Sokołowski. "TURNPIKE CONTROL AND STATIC FINITE-PARAMETER SHAPE DESIGN FOR LINEAR ELASTODYNAMICS: A CONDITIONAL ANALYTICAL FRAMEWORK." Evolution Equations and Control Theory 26 (2026): 66-95.

BibTeX: Download