@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{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{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{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}

}