@article{Ortigosa2024b,

title = {Shape-programming in hyperelasticity through differential growth},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},

editor = {Springer},

url = {https://link.springer.com/10.1007/s00245-024-10117-6?utm_source=rct_congratemailt&utm_medium=email&utm_campaign=oa_20240323&utm_content=10.1007/s00245-024-10117-6},

doi = {10.1007/s00245-024-10117-6},

issn = {1432-0606},

year  = {2024},

date = {2024-03-23},

urldate = {2024-12-01},

journal = {Applied Mathematics and Optimization},

volume = {89},

number = {49},

abstract = {This paper is concerned with the growth-driven shape-programming problem, which involves determining a growth tensor that can produce a deformation on a hyperelastic body reaching a given target shape. We consider the two cases of globally compatible growth, where the growth tensor is a deformation gradient over the undeformed domain, and the incompatible one, which discards such hypothesis. We formulate the problem within the framework of optimal control theory in hyperelasticity. The Hausdorff distance is used to quantify dissimilarities between shapes; the complexity of the actuation is incorporated in the cost functional as well. Boundary conditions and external loads are allowed in the state law, thus extending previous works where the stress-free hypothesis turns out to be essential. A rigorous mathematical analysis is then carried out to prove the well-posedness of the problem. The numerical approximation is performed using gradient-based optimisation algorithms. Our main goal in this part is to show the possibility to apply inverse techniques for the numerical approximation of this problem, which allows us to address more generic situations than those covered by analytical approaches. Several numerical experiments for beam-like and shell-type geometries illustrate the performance of the proposed numerical scheme.},

keywords = {21996/PI/22},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2024,

title = {Probability-of-failure-based optimization for Random pdes through concentration-of-measure Inequalities},

author = {Rogelio Ortigosa and Jesus Martinez-Frutos and Francisco Periago},

doi = {doi.org/10.1051/cocv/2023075},

year  = {2024},

date = {2024-03-01},

urldate = {2024-03-01},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

abstract = {Control and optimization problems constrained by partial differential equations (PDEs)

with random input data and that incorporate probabilities of failure in their formulations are numerically

extremely challenging, since the computational cost of estimating the tails of a probability

distribution is prohibitive in many situations encountered in real-life engineering problems. In addition,

probabilities of failure are often discontinuous and include huge flat regions where gradients vanish.

Based on the McDiarmid concentration-of-measure inequality, this paper proposes a new functional

which provides a tight and smooth bound for the probability of a given random functional of exceeding

a prescribed threshold parameter. Hence, this approach relieves the above-mentioned difficulties in

the case where the solution map is convex with respect to the random parameter, as in the case of

a deterministic differential operator and the random parameter appearing linearly in the right-hand

side term. Well-posedness of the corresponding optimal control problem is established and the viability

of the proposed method is numerically illustrated by two benchmarks examples arising in topology

optimization and optimal control theory.},

keywords = {21996/PI/22},

pubstate = {forthcoming},

tppubtype = {article}

}

@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}

}

@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}

}

@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}

}

@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}

}

@article{Martínez-Frutos2018b,

title = {Structural optimization under internal porosity constraints using topological derivatives},

author = {Jesús Martínez-Frutos and Grégoire Allaire and Charles Dapogny and Francisco Periago},

url = {https://hal.archives-ouvertes.fr/hal-01790472v1 

https://www.sciencedirect.com/science/article/pii/S0045782518305401},

doi = {https://doi.org/10.1016/j.cma.2018.10.036},

year  = {2019},

date = {2019-01-01},

urldate = {2019-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {345},

pages = {1-25},

abstract = {Porosity is a well-known phenomenon occurring during various manufacturing processes (casting, welding, additive manufacturing) of solid structures, which undermines their reliability and mechanical performance. The main purpose of this article is to introduce a new constraint functional of the domain which controls the negative impact of porosity on elastic structures in the framework of shape and topology optimization. The main ingredient of our modeling is the notion of topological derivative, which is used in a slightly unusual way: instead of being an indicator of where to nucleate holes in the course of the optimization process, it is a component of a new constraint functional which assesses the influence of pores on the mechanical performance of structures. The shape derivative of this constraint is calculated and incorporated into a level set based shape optimization algorithm. Our approach is illustrated by several two- and three-dimensional numerical experiments of topology optimization problems constrained by a control on the porosity effect.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Marín2018b,

title = {A polynomial chaos-based approach to risk-averse piezoelectric control of random vibrations of beams},

author = {Francisco J. Marín and Jesús Martínez-Frutos and Francisco Periago},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5823},

issn = {1097-0207},

year  = {2018},

date = {2018-08-10},

urldate = {2018-08-10},

journal = {International Journal for Numerical Methods in Engineering},

volume = {115},

number = {6},

pages = {738-755},

abstract = {This paper proposes a risk-averse formulation for the problem of piezoelectric control of random vibrations of elastic structures. The proposed formulation, inspired by the notion of risk aversion in Economy, is applied to the piezoelectric control of a Bernoulli-Euler beam subjected to uncertainties in its input data. To address the high computational burden associated to the presence of random fields in the model and the discontinuities involved in the cost functional and its gradient, a combination of a non-intrusive anisotropic polynomial chaos approach for uncertainty propagation with a Monte Carlo sampling method is proposed. In a first part, the well-posedness of the control problem is established by proving the existence of optimal controls. In a second part, an adaptive gradient-based method is proposed for the numerical resolution of the problem. Several experiments illustrate the performance of the proposed approach and the significant differences that may occur between the classical deterministic formulation of the problem and its stochastic risk-averse counterpart.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Morales2017,

title = {Robust Optimal Design of Quantum Electronic Devices},

author = {Ociel Morales and Francisco Periago and José A. Vallejo},

url = {https://www.hindawi.com/journals/mpe/2018/3095257/abs/},

issn = {2331-8422},

year  = {2018},

date = {2018-04-05},

urldate = {2018-04-05},

journal = {Mathematical Problems in Engineering},

volume = {2018},

pages = {10},

abstract = {We consider the optimal design of a sequence of quantum barriers in order to manufacture an electronic device at the nanoscale such that the dependence of its transmission coefficient on the bias voltage is linear. The technique presented here is easily adaptable to other response characteristics. The transmission coefficient is computed using the Wentzel-Kramers-Brillouin (WKB) method, so we can explicitly compute the gradient of the objective function. In contrast with earlier treatments, manufacturing uncertainties are incorporated in the model through random variables and the optimal design problem is formulated in a probabilistic setting. As a measure of robustness, a weighted sum of the expectation and the variance of a least-squares performance metric is considered. Several simulations illustrate the proposed approach.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{JMF_CMAME_2017,

title = {Risk-averse structural topology optimization under random fields using stochastic expansion methods},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

url = {https://www.sciencedirect.com/science/article/pii/S0045782517306990 

http://www.upct.es/mc3/files/JMF/riskaverse_cmame.pdf},

issn = {0045-7825},

year  = {2018},

date = {2018-03-01},

urldate = {2018-03-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {330},

pages = {180-206},

abstract = {This work proposes a level-set based approach for solving risk-averse structural topology optimization problems considering random field loading and material uncertainty. The use of random fields increases the dimensionality of the stochastic domain, which poses several computational challenges related to the minimization of the Excess Probability as a measure of risk awareness. This problem is addressed both from the theoretical and numerical viewpoints. First, an existence result under a typical geometrical constraint on the set of admissible shapes is proved. Second, a level-set continuous approach to find the numerical solution of the problem is proposed. Since the considered cost functional has a discontinuous integrand, the numerical approximation of the functional and its sensitivity combine an adaptive anisotropic Polynomial Chaos (PC) approach with a Monte-Carlo (MC) sampling method for uncertainty propagation. Furthermore, to address the increment of dimensionality induced by the random field, an anisotropic sparse grid stochastic collocation method is used for the efficient computation of the PC coefficients. A key point is that the non-intrusive nature of such an approach facilitates the use of High Performance Computing (HPC) to alleviate the computational burden of the problem. Several numerical experiments including random field loading and material uncertainty are presented to show the feasibility of the proposal.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Marín2017,

title = {Robust Averaged Control of Vibrations for the Bernoulli-Euler Beam Equation},

author = {Francisco J. Marín and Jesús Martínez-Frutos and Francisco Periago},

url = {https://doi.org/10.1007/s10957-017-1128-x 

http://localhost/mc3/files/FPE/marin_17.pdf},

doi = {10.1007/s10957-017-1128-x},

issn = {1573-2878},

year  = {2017},

date = {2017-08-01},

urldate = {2017-08-01},

journal = {Journal of Optimization Theory and Applications},

volume = {174},

number = {2},

pages = {428–454},

abstract = {This paper proposes an approach for the robust averaged control of random vibrations for the Bernoulli–Euler beam equation under uncertainty in the flexural stiffness and in the initial conditions. The problem is formulated in the framework of optimal control theory and provides a functional setting, which is so general as to include different types of random variables and second-order random fields as sources of uncertainty. The second-order statistical moment of the random system response at the control time is incorporated in the cost functional as a measure of robustness. The numerical resolution method combines a classical descent method with an adaptive anisotropic stochastic collocation method for the numerical approximation of the statistics of interest. The direct and adjoint stochastic systems are uncoupled, which permits to exploit parallel computing architectures to solve the set of deterministic problem that arise from the stochastic collocation method. As a result, problems with a relative large number of random variables can be solved with a reasonable computational cost. Two numerical experiments illustrate both the performance of the proposed method and the significant differences that may occur when uncertainty is incorporated in this type of control problems.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{NME:NME5210,

title = {Robust optimal Robin boundary control for the transient heat equation with random input data},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Arnaud Münch and Francisco Periago},

url = {http://dx.doi.org/10.1002/nme.5210 

http://localhost/mc3/files/FPE/ijnme_16.pdf},

doi = {10.1002/nme.5210},

issn = {1097-0207},

year  = {2016},

date = {2016-03-02},

urldate = {2016-03-02},

journal = {International Journal for Numerical Methods in Engineering},

volume = {108},

number = {2},

pages = {116–135},

abstract = {The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient-based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analysed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2016271,

title = {Robust shape optimization of continuous structures via the level set method},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

url = {http://www.sciencedirect.com/science/article/pii/S0045782516300834 

http://localhost/mc3/files/FPE/cmame16.pdf},

doi = {https://doi.org/10.1016/j.cma.2016.03.003},

issn = {0045-7825},

year  = {2016},

date = {2016-01-15},

urldate = {2016-01-15},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {305},

number = {Supplement C},

pages = {271 - 291},

abstract = {Abstract This work proposes a stochastic shape optimization method for continuous structures using the level-set method. Such a method aims to minimize the expected compliance and its variance as measures of the structural robustness. The behavior of continuous structures is modeled by linear elasticity equations with uncertain loading and material. This uncertainty can be modeled using random variables with different probability distributions as well as random fields. The proper problem formulation is ensured by the proof of the existence colorrev of solution under certain geometrical constraints on the set of admissible shapes. The proposed method addresses the stochastic linear elasticity problem in its weak form obtaining the explicit expressions for the continuous shape derivatives. Some numerical examples are presented to show the effectiveness of the proposed approach.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2015,

title = {Robust optimal shape design for an elliptic PDE with uncertainty in its input data},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

doi = {10.1051/cocv/2014049},

issn = {1262-3377},

year  = {2015},

date = {2015-05-20},

urldate = {2015-05-20},

journal = {ESAIM: COCV},

volume = {21},

number = {4},

pages = {901--923},

publisher = {EDP Sciences},

keywords = {19274/PI/14, Computational Mathematics, Control and Optimization, Control and Systems Engineering},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@article{Münch2013,

title = {Numerical approximation of bang–bang controls for the heat equation: An optimal design approach},

author = {Arnaud Münch and Francisco Periago},

doi = {10.1016/j.sysconle.2013.04.009},

issn = {0167-6911},

year  = {2013},

date = {2013-08-00},

urldate = {2013-08-00},

journal = {Systems & Control Letters},

volume = {62},

number = {8},

pages = {643--655},

publisher = {Elsevier BV},

keywords = {Control and Systems Engineering, Electrical and Electronic Engineering, General Computer Science, Mechanical Engineering},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@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}

}

@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}

}

@article{Münch2008,

title = {Optimal Internal Stabilization of the Linear System of Elasticity},

author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},

doi = {10.1007/s00205-008-0187-4},

issn = {1432-0673},

year  = {2009},

date = {2009-07-00},

urldate = {2009-07-00},

journal = {Arch Rational Mech Anal},

volume = {193},

number = {1},

pages = {171--193},

publisher = {Springer Science and Business Media LLC},

keywords = {Analysis, Mathematics (miscellaneous), Mechanical Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2009,

title = {Optimal shape and position of the support for the internal exact control of a string},

author = {Francisco Periago},

doi = {10.1016/j.sysconle.2008.08.007},

issn = {0167-6911},

year  = {2009},

date = {2009-02-00},

urldate = {2009-02-00},

journal = {Systems & Control Letters},

volume = {58},

number = {2},

pages = {136--140},

publisher = {Elsevier BV},

keywords = {Control and Systems Engineering, Electrical and Electronic Engineering, General Computer Science, Mechanical Engineering},

pubstate = {published},

tppubtype = {article}

}

@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}

}

@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{Münch2006,

title = {A variational approach to a shape design problem for the wave equation},

author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},

doi = {10.1016/j.crma.2006.07.013},

issn = {1631-073X},

year  = {2006},

date = {2006-09-00},

urldate = {2006-09-00},

journal = {Comptes Rendus Mathematique},

volume = {343},

number = {5},

pages = {371--376},

publisher = {Cellule MathDoc/CEDRAM},

keywords = {General 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}

}

@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}

}

@article{Periago2003b,

title = {On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem},

author = {Francisco Periago and B. Straub},

doi = {10.4064/sm155-2-7},

issn = {1730-6337},

year  = {2003},

date = {2003-00-00},

urldate = {2003-00-00},

journal = {Studia Math.},

volume = {155},

number = {2},

pages = {183--193},

publisher = {Institute of Mathematics, Polish Academy of Sciences},

keywords = {General Mathematics},

pubstate = {published},

tppubtype = {article}

}