@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}

}