## Abstract

Engineering analysis requires the prediction of selected “outputs” s relevant to ultimate component and system performance; typical outputs include critical stresses or strains, flow rates or pressure drops, and various measures of temperature and heat flux. These outputs are functions of “inputs” μ that serve to identify a particular configuration of the component or system; typical inputs reflect geometry, properties, and boundary conditions and loads.

In many cases, the input-output function is best articulated as a (say) linear functional ℓ of a field variable u(μ) that is the solution to an input-parameterized partial differential equation (PDE); typical field variables and associated PDEs include temperature and steady/unsteady conduction, displacement and equilibrium elasticity/Helmholtz, and velocity and steady incompressible Navier—Stokes. System behavior is thus described by an input-output relation s(μ) = ℓ(u(μ)), the evaluation of which requires solution of the underlying PDE.

Our focus is on “deployed” systems—components or processes in operation in the field—and associated “Assess-Act” scenarios. In the Assess stage we pursue robust parameter estimation (inverse) procedures that map measured-observable outputs to (all) possible system-characteristic and environment-state inputs. In the subsequent Act stage we then pursue adaptive design (optimization) procedures that map mission-objective outputs to best control-variable inputs.

In many cases, the input-output function is best articulated as a (say) linear functional ℓ of a field variable u(μ) that is the solution to an input-parameterized partial differential equation (PDE); typical field variables and associated PDEs include temperature and steady/unsteady conduction, displacement and equilibrium elasticity/Helmholtz, and velocity and steady incompressible Navier—Stokes. System behavior is thus described by an input-output relation s(μ) = ℓ(u(μ)), the evaluation of which requires solution of the underlying PDE.

Our focus is on “deployed” systems—components or processes in operation in the field—and associated “Assess-Act” scenarios. In the Assess stage we pursue robust parameter estimation (inverse) procedures that map measured-observable outputs to (all) possible system-characteristic and environment-state inputs. In the subsequent Act stage we then pursue adaptive design (optimization) procedures that map mission-objective outputs to best control-variable inputs.

Original language | English |
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Title of host publication | Real-Time PDE-Constrained Optimization |

Editors | Lorentz T. Biegler , Omar Ghattas, Matthias Heinkenschloss, David Keyes, Bart van Bloemen Waanders |

Place of Publication | Philadelphia |

Publisher | Society for Industrial and Applied Mathematics (SIAM) |

Chapter | 10 |

Pages | 199-216 |

Number of pages | 18 |

ISBN (Electronic) | 9780898718935 |

ISBN (Print) | 9780898716214 |

DOIs | |

Publication status | Published - 2007 |

Externally published | Yes |

### Publication series

Name | Computational Science & Engineering |
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Publisher | Society for Industrial and Applied Mathematics |

Volume | 3 |

## Keywords

- optimal control
- parameter estimation
- real-time optimization
- partial differential equations
- science and engineering applications