Dr. Francisco Periago
Full Professor, Applied Mathematics
RESEARCH LINKS
- OrcID: 0000-0002-7323-1809
- Scopus Author ID: 14069164900
- MathScinet: 1091151
- ETSII Office B023. Campus Muralla del Mar. Hospital de Marina. C/ Dr. Fleming SN. 30202 Cartagena
- Phone: +34 968338909
- Email: [email protected]
- Available For Postgraduate Supervision
ABOUT
I hold a Doctorate in Applied Mathematics from the University of Valencia, Spain, conferred in 1999. Notably, I served as the principal investigator in two I+D+i contracts with Navantia S.A (2007-2012), facilitating the funding of a predoctoral scholarship and a predoctoral research contract. This endeavor resulted in the submission of two PhD theses and the creation of the software SIMUSUB, presently employed at Navantia. Additionally, I have delivered keynote addresses at various national (e.g., XXVII CEDYA/XVII CMA, held in Zaragoza in 2022) and international congresses and workshops (e.g., at the esteemed Institute Henri Poincaré, Paris).
My academic engagements extend globally, having served as a visiting researcher at multiple esteemed institutions: (1) School of Mathematics, University of New South Wales (Australia, 3 months in 2000); (2) Instituto de Matemática - Laboratorio Nacional de Computación, Rio de Janeiro (Brazil, 6 weeks in 2003); (3) Departament de Mathématiques, Université de Franche-Comté (France, several short visits between 2006-2010); (4) École Polytechnique de Paris (France, several short visits between 2008-2014); (5) Mathematics Department, University of California, Santa Barbara (USA, 4 months in 2021). Furthermore, my research contributions have been recognized through successive periods of research activity (Sexenios de investigación y transferencia), totaling five periods, with the latest spanning from 2016 to 2021.
AREAS OF EXPERTISE
- Optimal Control and Design of PDEs
- Stochastic PDEs
- Robust and Risk-averse design
- Topology Optimization
- Physics-informed Neural Networks
- Shape control in Finite Strains
PUBLICATIONS
Ortigosa, Rogelio; Martínez-Frutos, Jesús; Mora-Corral, Carlos; Pedregal, Pablo; Periago, Francisco Mathematical modeling, analysis and control in soft robotics: a survey Journal Article In: SeMA, 2023, ISSN: 2281-7875. Abstract | BibTeX | Tags: Applied Mathematics, Control and Optimization, DICOPMA, Modeling and Simulation, Numerical Analysis | Links: Ortigosa, Rogelio; Martínez-Frutos, Jesús; Mora-Corral, Carlos; Pedregal, Pablo; Periago, Francisco Optimal control and design of magnetic field-responsive smart polymer composites Journal Article In: Applied Mathematical Modelling, vol. 103, pp. 141-161, 2022, ISSN: 0307-904X. Abstract | BibTeX | Tags: DICOPMA, Hard-magnetic soft materials, Magneto-elasticity, Optimal control, Optimal design, Polyconvexity, Shape-morphing | Links: Ortigosa, Rogelio; Martínez-Frutos, Jesús; Mora-Corral, Carlos; Pedregal, Pablo; Periago, Francisco Optimal Control of Soft Materials Using a Hausdorff Distance Functional Journal Article In: SIAM Journal on Control and Optimization, vol. 59, no. 1, pp. 393-416, 2021. Abstract | BibTeX | Tags: DICOPMA | Links: Martínez-Frutos, Jesus; Ortigosa, Rogelio; Pedregal, Pablo; Periago, Francisco Robust optimal control of stochastic hyperelastic materials Journal Article In: Applied Mathematical Modelling, vol. 88, pp. 888-904, 2020, ISSN: 0307-904X. Abstract | BibTeX | Tags: Active fibers, DICOPMA, Hyperelasticity, Material uncertainty, Robust optimal control, Soft robotics, Turgor pressure | Links: 2023
@article{Ortigosa-Martínez2023,
title = {Mathematical modeling, analysis and control in soft robotics: a survey},
author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},
doi = {10.1007/s40324-023-00334-4},
issn = {2281-7875},
year = {2023},
date = {2023-08-04},
urldate = {2023-08-04},
journal = {SeMA},
publisher = {Springer Science and Business Media LLC},
abstract = {<jats:title>Abstract</jats:title><jats:p>This paper reviews some recent advances in mathematical modeling, analysis and control, both from the theoretical and numerical viewpoints, in the emergent field of soft robotics. The presentation is not focused on specific prototypes of soft robots, but in a more general description of soft smart materials. The goal is to provide a unified and rigorous mathematical approach to open-loop control strategies for soft materials that hopefully might lay the seeds for future research in this field.</jats:p>},
keywords = {Applied Mathematics, Control and Optimization, DICOPMA, Modeling and Simulation, Numerical Analysis},
pubstate = {published},
tppubtype = {article}
}
2022
@article{ORTIGOSA2022141,
title = {Optimal control and design of magnetic field-responsive smart polymer composites},
author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},
url = {https://www.sciencedirect.com/science/article/pii/S0307904X21005096},
doi = {https://doi.org/10.1016/j.apm.2021.10.033},
issn = {0307-904X},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
journal = {Applied Mathematical Modelling},
volume = {103},
pages = {141-161},
abstract = {This paper presents a novel in-silico framework for the simultaneous optimal control and design of complex magnetic responsive polymer composite materials. State-of-the-art optimisation techniques are used in conjunction with the latest developments in the numerical solution of hard-magnetic soft materials undergoing large (potentially extreme) deformations, in order to address the challenging task of designing shape-morphing two-dimensional composite magnetic sheets. This paper introduces the following key novelties: (i) an optimisation-driven method for the simultaneous optimal control and design of the externally applied magnetic flux density as well as the remnant magnetisation of hard particles within the elastomer matrix, (ii) the well-posedness character of the optimisation problem is established by proving existence of solutions for both the underlying state equation and the control problem itself, (iii) a gradient-based optimisation algorithm is proposed for the numerical approximation of the problem, where explicit expressions of the continuous gradients are obtained by using the formal Lagrangian method. Furthermore, a series of numerical examples are presented in order to demonstrate the capability of the proposal as an alternative to intuition or experimentally-based approaches, representing an optimisation-driven method that facilitates the design of smart materials yielding complex magnetically induced shape morphing configurations.},
keywords = {DICOPMA, Hard-magnetic soft materials, Magneto-elasticity, Optimal control, Optimal design, Polyconvexity, Shape-morphing},
pubstate = {published},
tppubtype = {article}
}
2021
@article{doi:10.1137/19M1307299,
title = {Optimal Control of Soft Materials Using a Hausdorff Distance Functional},
author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},
url = {https://doi.org/10.1137/19M1307299},
doi = {10.1137/19M1307299},
year = {2021},
date = {2021-01-01},
urldate = {2021-01-01},
journal = {SIAM Journal on Control and Optimization},
volume = {59},
number = {1},
pages = {393-416},
abstract = {This paper addresses, from both theoretical and numerical standpoints, the problem of optimal control of hyperelastic materials characterized by means of polyconvex stored energy functionals. Specifically, inspired by Günnel and Herzog [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 tracking-type cost functionals alternative to those generally used in this field, where the $L^2$ 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 regularized 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 emphasized that in contrast to $L^2$ 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.},
keywords = {DICOPMA},
pubstate = {published},
tppubtype = {article}
}
2020
@article{MARTINEZFRUTOS2020888,
title = {Robust optimal control of stochastic hyperelastic materials},
author = {Jesus Martínez-Frutos and Rogelio Ortigosa and Pablo Pedregal and Francisco Periago},
url = {https://www.sciencedirect.com/science/article/pii/S0307904X20303772},
doi = {https://doi.org/10.1016/j.apm.2020.07.012},
issn = {0307-904X},
year = {2020},
date = {2020-01-01},
urldate = {2020-01-01},
journal = {Applied Mathematical Modelling},
volume = {88},
pages = {888-904},
abstract = {Soft robots are highly nonlinear systems made of deformable materials such as elastomers, fluids and other soft matter, that often exhibit intrinsic uncertainty in their elastic responses under large strains due to microstructural inhomogeneity. These sources of uncertainty might cause a change in the dynamics of the system leading to a significant degree of complexity in its controllability. This issue poses theoretical and numerical challenges in the emerging field of optimal control of stochastic hyperelasticity. This paper states and solves the robust averaged control in stochastic hyperelasticity where the underlying state system corresponds to the minimization of a stochastic polyconvex strain energy function. Two bio-inspired optimal control problems under material uncertainty are addressed. The expected value of the L2-norm to a given target configuration is minimized to reduce the sensitivity of the spatial configuration to variations in the material parameters. The existence of optimal solutions for the robust averaged control problem is proved. Then the problem is solved numerically by using a gradient-based method. Two numerical experiments illustrate both the performance of the proposed method to ensure the robustness of the system and the significant differences that may occur when uncertainty is incorporated in this type of control problems.},
keywords = {Active fibers, DICOPMA, Hyperelasticity, Material uncertainty, Robust optimal control, Soft robotics, Turgor pressure},
pubstate = {published},
tppubtype = {article}
}