Optimal control of soft materials using a hausdorff distance functional
Entity
UAM. Departamento de MatemáticasPublisher
Society for Industrial and Applied MathematicsDate
2021-01-20Citation
10.1137/19M1307299
SIAM Journal on Control and Optimization 59.1 (2021): 393-416
ISSN
0363-0129 (print); 1095-7138 (online)DOI
10.1137/19M1307299Funded by
This work was funded by the Spanish Ministerio de Economía y Competitividad through grants MTM2017-83740-P and MTM2017-85934-C3-2-P, and by Fundación Séneca (Agencia de Ciencia y Tecnología de la Región de Murcia (Spain)) under the contract 20911/PI/18. P.P. acknowledges the support of grant 2019-GRIN-26890 of U. de Castilla-La ManchaProject
Gobierno de España. MTM2017-83740-P; Gobierno de España. MTM2017-85934-C3-2-PEditor's Version
https://doi.org/10.1137/19M1307299Subjects
Hausdorff distance; Hyperelasticity; Optimal control; Soft robotics; MatemáticasRights
© 2021, Society for Industrial and Applied MathematicsAbstract
This paper addresses, from both theoretical and numerical standpoints, the problem of optimal control of hyperelastic materials characterised by means of polyconvex stored energy functionals. Specifically, inspired by A. Günnel and R. Herzog, Optimal control problems in finite strain elasticity by inner pressure and fiber tension. Front. Appl. Math. Stat., 2 (2016, a bio-inspired type of external action or control, which resembles the electro-activation mechanism of the human heart, is considered in this paper. The main contribution resides in the consideration of alternative tracking-type cost functionals to those generally used in this field, where the L2 norm of the distance to a given target displacement field is the preferred option. Alternatively, the Hausdorff metric is, for the first time, explored in the context of optimal control in hyperelasticity. The existence of a solution for a regularised version of the optimal control problem is proved. A gradient-based method, which makes use of the concept of shape derivative, is proposed as a numerical resolution method. A series of numerical examples are included illustrating the viability and applicability of the Hausdorff metric in this new context. Furthermore, although not pursued in this paper, it must be emphasised that in contrast to L2 norm tracking-cost functional types, the Hausdorff metric permits the use of potentially very different computational domains for both the target and the actuated soft continuum
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Google Scholar:Ortigosa, Rogelio
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Martinez-Frutos, Jesus
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Mora Corral, Carlos
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Pedregal, Pablo
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Periago, Francisco
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