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: García-Cervera, Carlos J.; Kessler, Mathieu; Periago, Francisco Control of Partial Differential Equations via Physics-Informed Neural Networks Journal Article In: J Optim Theory Appl, vol. 196, no. 2, pp. 391–414, 2023, ISSN: 1573-2878. Abstract | BibTeX | Tags: Applied Mathematics, Control and Optimization, Management Science and Operations Research | Links: Periago, Francisco Optimal Design of the Time-Dependent Support of Bang–Bang Type Controls for the Approximate Controllability of the Heat Equation Journal Article In: J Optim Theory Appl, vol. 161, no. 3, pp. 951–968, 2014, ISSN: 1573-2878. BibTeX | Tags: Applied Mathematics, Control and Optimization, Management Science and Operations Research | Links: Font, Roberto; Pedregal, Pablo; Periago, Francisco A numerical method for computing optimal controls in feedback and digital forms and its application to the blowing‐venting control system of manned submarines Journal Article In: Optim Control Appl Methods, vol. 34, no. 2, pp. 236–252, 2013, ISSN: 1099-1514. Abstract | BibTeX | Tags: Applied Mathematics, Control and Optimization, Control and Systems Engineering, Software | Links: Ovalle, Diana M.; García, Javier; Periago, Francisco Analysis and numerical simulation of a nonlinear mathematical model for testing the manoeuvrability capabilities of a submarine Journal Article In: Nonlinear Analysis: Real World Applications, vol. 12, no. 3, pp. 1654–1669, 2011, ISSN: 1468-1218. BibTeX | Tags: Analysis, Applied Mathematics, Computational Mathematics, Econometrics and Finance, General Economics, General Engineering, General Medicine | Links: Münch, Arnaud; Periago, Francisco Optimal distribution of the internal null control for the one-dimensional heat equation Journal Article In: Journal of Differential Equations, vol. 250, no. 1, pp. 95–111, 2011, ISSN: 0022-0396. BibTeX | Tags: Analysis, Applied Mathematics | Links: Font, Roberto; Periago, Francisco Numerical simulation of the boundary exact control for the system of linear elasticity Journal Article In: Applied Mathematics Letters, vol. 23, no. 9, pp. 1021–1026, 2010, ISSN: 0893-9659. BibTeX | Tags: Applied Mathematics | Links: Periago, Francisco; Tiago, Jorge A local existence result for an optimal control problem modeling the manoeuvring of an underwater vehicle Journal Article In: Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 2573–2583, 2010, ISSN: 1468-1218. BibTeX | Tags: Analysis, Applied Mathematics, Computational Mathematics, Econometrics and Finance, General Economics, General Engineering, General Medicine | Links: Allaire, Grégoire; Münch, Arnaud; Periago, Francisco Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation Journal Article In: SIAM J. Control Optim., vol. 48, no. 8, pp. 5333–5356, 2010, ISSN: 1095-7138. BibTeX | Tags: Applied Mathematics, Control and Optimization | Links: Pedregal, Pablo; Periago, Francisco; Villena, Jorge A Numerical Method of Local Energy Decay for the Boundary Controllability of Time‐Reversible Distributed Parameter Systems Journal Article In: Stud Appl Math, vol. 121, no. 1, pp. 27–47, 2008, ISSN: 1467-9590. Abstract | BibTeX | Tags: Applied Mathematics | Links: Münch, Arnaud; Pedregal, Pablo; Periago, Francisco Relaxation of an optimal design problem for the heat equation Journal Article In: Journal de Mathématiques Pures et Appliquées, vol. 89, no. 3, pp. 225–247, 2008, ISSN: 0021-7824. BibTeX | Tags: Applied Mathematics, General Mathematics | Links: Münch, Arnaud; Pedregal, Pablo; Periago, Francisco Optimal design of the damping set for the stabilization of the wave equation Journal Article In: Journal of Differential Equations, vol. 231, no. 1, pp. 331–358, 2006, ISSN: 0022-0396. BibTeX | Tags: Analysis, Applied Mathematics | Links: Pedregal, Pablo; Periago, Francisco Some remarks on homogenization and exact boundary controllability for the one-dimensional wave equation Journal Article In: Quart. Appl. Math., vol. 64, no. 3, pp. 529–546, 2006, ISSN: 1552-4485. Abstract | BibTeX | Tags: Applied Mathematics | Links: Periago, Francisco Global existence, uniqueness, and continuous dependence for a semilinear initial value problem Journal Article In: Journal of Mathematical Analysis and Applications, vol. 280, no. 2, pp. 413–423, 2003, ISSN: 0022-247X. BibTeX | Tags: Analysis, Applied Mathematics | Links: Periago, Francisco Global existence, uniqueness, and continuous dependence for a semilinear initial value problem Journal Article In: Journal of Mathematical Analysis and Applications, vol. 280, no. 2, pp. 413–423, 2003, ISSN: 0022-247X. BibTeX | Tags: Analysis, Applied Mathematics | 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}
}
@article{García-Cervera2022,
title = {Control of Partial Differential Equations via Physics-Informed Neural Networks},
author = {Carlos J. García-Cervera and Mathieu Kessler and Francisco Periago},
url = {https://link.springer.com/content/pdf/10.1007/s10957-022-02100-4.pdf},
doi = {10.1007/s10957-022-02100-4},
issn = {1573-2878},
year = {2023},
date = {2023-02-00},
urldate = {2023-02-00},
journal = {J Optim Theory Appl},
volume = {196},
number = {2},
pages = {391--414},
publisher = {Springer Science and Business Media LLC},
abstract = {<jats:title>Abstract</jats:title><jats:p>This paper addresses the numerical resolution of controllability problems for partial differential equations (PDEs) by using physics-informed neural networks. Error estimates for the generalization error for both state and control are derived from classical observability inequalities and energy estimates for the considered PDE. These error bounds, that apply to any exact controllable linear system of PDEs and in any dimension, provide a rigorous justification for the use of neural networks in this field. Preliminary numerical simulation results for three different types of PDEs are carried out to illustrate the performance of the proposed methodology.</jats:p>},
keywords = {Applied Mathematics, Control and Optimization, Management Science and Operations Research},
pubstate = {published},
tppubtype = {article}
}
2014
@article{Periago2013,
title = {Optimal Design of the Time-Dependent Support of Bang–Bang Type Controls for the Approximate Controllability of the Heat Equation},
author = {Francisco Periago},
doi = {10.1007/s10957-013-0447-9},
issn = {1573-2878},
year = {2014},
date = {2014-06-00},
urldate = {2014-06-00},
journal = {J Optim Theory Appl},
volume = {161},
number = {3},
pages = {951--968},
publisher = {Springer Science and Business Media LLC},
keywords = {Applied Mathematics, Control and Optimization, Management Science and Operations Research},
pubstate = {published},
tppubtype = {article}
}
2013
@article{Font2012,
title = {A numerical method for computing optimal controls in feedback and digital forms and its application to the blowing‐venting control system of manned submarines},
author = {Roberto Font and Pablo Pedregal and Francisco Periago},
doi = {10.1002/oca.2024},
issn = {1099-1514},
year = {2013},
date = {2013-03-00},
urldate = {2013-03-00},
journal = {Optim Control Appl Methods},
volume = {34},
number = {2},
pages = {236--252},
publisher = {Wiley},
abstract = {<jats:title>SUMMARY</jats:title><jats:p>On the basis of the classical variational reformulation of optimal control problems, we introduce a numerical scheme for solving those problems where the goal is the computation of optimal controls in feedback and digital forms defined on a discrete time mesh. The algorithm reduces the computation of such controls to solving a suitable nonlinear mathematical programming problem where the unknowns are the controls and slope of the state variable of the original problem. The motivation for this study comes from the real‐world engineering problem which consists of maneuvering a manned submarine by using the blowing‐venting control system of the ballast tanks of the vehicle. After checking the proposed algorithm in an academic example, we apply it to the maneuvering problem of submarines whose mathematical model includes a state law which is composed of a system of twenty‐four nonlinear ordinary differential equations. Numerical results illustrate the performance of the numerical scheme. Copyright © 2012 John Wiley & Sons, Ltd.</jats:p>},
keywords = {Applied Mathematics, Control and Optimization, Control and Systems Engineering, Software},
pubstate = {published},
tppubtype = {article}
}
2011
@article{Ovalle2011,
title = {Analysis and numerical simulation of a nonlinear mathematical model for testing the manoeuvrability capabilities of a submarine},
author = {Diana M. Ovalle and Javier García and Francisco Periago},
doi = {10.1016/j.nonrwa.2010.11.001},
issn = {1468-1218},
year = {2011},
date = {2011-06-00},
urldate = {2011-06-00},
journal = {Nonlinear Analysis: Real World Applications},
volume = {12},
number = {3},
pages = {1654--1669},
publisher = {Elsevier BV},
keywords = {Analysis, Applied Mathematics, Computational Mathematics, Econometrics and Finance, General Economics, General Engineering, General Medicine},
pubstate = {published},
tppubtype = {article}
}
@article{Münch2011,
title = {Optimal distribution of the internal null control for the one-dimensional heat equation},
author = {Arnaud Münch and Francisco Periago},
doi = {10.1016/j.jde.2010.10.020},
issn = {0022-0396},
year = {2011},
date = {2011-01-00},
urldate = {2011-01-00},
journal = {Journal of Differential Equations},
volume = {250},
number = {1},
pages = {95--111},
publisher = {Elsevier BV},
keywords = {Analysis, Applied Mathematics},
pubstate = {published},
tppubtype = {article}
}
2010
@article{Font2010,
title = {Numerical simulation of the boundary exact control for the system of linear elasticity},
author = {Roberto Font and Francisco Periago},
doi = {10.1016/j.aml.2010.04.030},
issn = {0893-9659},
year = {2010},
date = {2010-09-00},
urldate = {2010-09-00},
journal = {Applied Mathematics Letters},
volume = {23},
number = {9},
pages = {1021--1026},
publisher = {Elsevier BV},
keywords = {Applied Mathematics},
pubstate = {published},
tppubtype = {article}
}
@article{Periago2010,
title = {A local existence result for an optimal control problem modeling the manoeuvring of an underwater vehicle},
author = {Francisco Periago and Jorge Tiago},
doi = {10.1016/j.nonrwa.2009.09.002},
issn = {1468-1218},
year = {2010},
date = {2010-08-00},
urldate = {2010-08-00},
journal = {Nonlinear Analysis: Real World Applications},
volume = {11},
number = {4},
pages = {2573--2583},
publisher = {Elsevier BV},
keywords = {Analysis, Applied Mathematics, Computational Mathematics, Econometrics and Finance, General Economics, General Engineering, General Medicine},
pubstate = {published},
tppubtype = {article}
}
@article{Allaire2010,
title = {Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation},
author = {Grégoire Allaire and Arnaud Münch and Francisco Periago},
doi = {10.1137/090780481},
issn = {1095-7138},
year = {2010},
date = {2010-01-00},
urldate = {2010-01-00},
journal = {SIAM J. Control Optim.},
volume = {48},
number = {8},
pages = {5333--5356},
publisher = {Society for Industrial & Applied Mathematics (SIAM)},
keywords = {Applied Mathematics, Control and Optimization},
pubstate = {published},
tppubtype = {article}
}
2008
@article{Pedregal2008,
title = {A Numerical Method of Local Energy Decay for the Boundary Controllability of Time‐Reversible Distributed Parameter Systems},
author = {Pablo Pedregal and Francisco Periago and Jorge Villena},
doi = {10.1111/j.1467-9590.2008.00406.x},
issn = {1467-9590},
year = {2008},
date = {2008-07-00},
urldate = {2008-07-00},
journal = {Stud Appl Math},
volume = {121},
number = {1},
pages = {27--47},
publisher = {Wiley},
abstract = {<jats:p>This paper deals with the numerical computation of the boundary controls of linear, time‐reversible, second‐order evolution systems. Based on a method introduced by Russell (<jats:italic>Stud. Appl. Math.</jats:italic> LII(3) (1973)) for the wave equation, a numerical algorithm is proposed for solving this type of problems. The convergence of the method is based on the local energy decay of the solution of a suitable Cauchy problem associated with the original control system. The method is illustrated with several numerical simulations for the Klein–Gordon and the Euler–Bernoulli equations in 1D, the wave equation on a rectangle, and the plate equation on a disk.</jats:p>},
keywords = {Applied Mathematics},
pubstate = {published},
tppubtype = {article}
}
@article{Münch2008b,
title = {Relaxation of an optimal design problem for the heat equation},
author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},
doi = {10.1016/j.matpur.2007.12.009},
issn = {0021-7824},
year = {2008},
date = {2008-03-00},
urldate = {2008-03-00},
journal = {Journal de Mathématiques Pures et Appliquées},
volume = {89},
number = {3},
pages = {225--247},
publisher = {Elsevier BV},
keywords = {Applied Mathematics, General Mathematics},
pubstate = {published},
tppubtype = {article}
}
2006
@article{Münch2006b,
title = {Optimal design of the damping set for the stabilization of the wave equation},
author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},
doi = {10.1016/j.jde.2006.06.009},
issn = {0022-0396},
year = {2006},
date = {2006-12-00},
urldate = {2006-12-00},
journal = {Journal of Differential Equations},
volume = {231},
number = {1},
pages = {331--358},
publisher = {Elsevier BV},
keywords = {Analysis, Applied Mathematics},
pubstate = {published},
tppubtype = {article}
}
@article{Pedregal2006,
title = {Some remarks on homogenization and exact boundary controllability for the one-dimensional wave equation},
author = {Pablo Pedregal and Francisco Periago},
doi = {10.1090/s0033-569x-06-01022-4},
issn = {1552-4485},
year = {2006},
date = {2006-09-00},
urldate = {2006-09-00},
journal = {Quart. Appl. Math.},
volume = {64},
number = {3},
pages = {529--546},
publisher = {American Mathematical Society (AMS)},
abstract = {<p>This paper contains three results concerning the homogenization and exact controllability for the one-dimensional wave equation. First, we give sufficient conditions on the initial data to ensure the convergence of the conormal derivatives associated with the wave equation with a rapidly oscillating coefficient and zero Dirichlet boundary conditions. Secondly, we apply this result to prove the existence of a class of initial data whose associated boundary controls are uniformly bounded and obtain some information (in particular, its limit behavior) on this class of data. Finally, we prove that all initial data in <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared times upper H Superscript negative 1">
<mml:semantics>
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>×<!-- × --></mml:mo>
<mml:msup>
<mml:mi>H</mml:mi>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:mo>−<!-- − --></mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:annotation encoding="application/x-tex">L^2times H^{-1}</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> may be uniformly controlled but at the price of adding an internal feedback control in our system. The main advantage of this last procedure is that we have explicit formulae for both states and controls.</p>},
keywords = {Applied Mathematics},
pubstate = {published},
tppubtype = {article}
}
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared times upper H Superscript negative 1">
<mml:semantics>
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>×<!-- × --></mml:mo>
<mml:msup>
<mml:mi>H</mml:mi>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:mo>−<!-- − --></mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:annotation encoding="application/x-tex">L^2times H^{-1}</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> may be uniformly controlled but at the price of adding an internal feedback control in our system. The main advantage of this last procedure is that we have explicit formulae for both states and controls.</p>2003
@article{Periago2003,
title = {Global existence, uniqueness, and continuous dependence for a semilinear initial value problem},
author = {Francisco Periago},
doi = {10.1016/s0022-247x(03)00126-4},
issn = {0022-247X},
year = {2003},
date = {2003-04-00},
urldate = {2003-04-00},
journal = {Journal of Mathematical Analysis and Applications},
volume = {280},
number = {2},
pages = {413--423},
publisher = {Elsevier BV},
keywords = {Analysis, Applied Mathematics},
pubstate = {published},
tppubtype = {article}
}
@article{Periago2003c,
title = {Global existence, uniqueness, and continuous dependence for a semilinear initial value problem},
author = {Francisco Periago},
doi = {10.1016/s0022-247x(03)00126-4},
issn = {0022-247X},
year = {2003},
date = {2003-04-00},
journal = {Journal of Mathematical Analysis and Applications},
volume = {280},
number = {2},
pages = {413--423},
publisher = {Elsevier BV},
keywords = {Analysis, Applied Mathematics},
pubstate = {published},
tppubtype = {article}
}