DASOPT

Numerical optimal control of parabolic PDEs using DASOPT. This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by time-dependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differential-algebraic equations (DAEs) with a package for large scale optimization based on sequential quadratic programming (SQP). DASOPT is intended for the computation of the optimal control of time-dependent nonlinear systems of PDEs in two (and eventually three) spatial dimensions, including possible inequality constraints on the state variables.par By the use of either finite difference or finite element approximations to the spatial derivatives, the PDEs are converted into a large system of ordinary differential equations or DAEs. Special techniques are needed in order to solve this very large optimal control problem. The use of DASOPT is illustrated by its application to a nonlinear parabolic PDE boundary control problem in two spatial dimensions. Computational results with and without bounds on the state variables are presented.


References in zbMATH (referenced in 12 articles )

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  1. Hazra, Subhendu Bikash; Schulz, Volker: On efficient computation of the optimization problem arising in the inverse modeling of non-stationary multiphase multicomponent flow through porous media (2005)
  2. Kunoth, Angela: Fast iterative solution of saddle point problems in optimal control based on wavelets (2002)
  3. Bewley, Thomas R.; Moin, Parviz; Temam, Roger: DNS-based predictive control of turbulence: An optimal benchmark for feedback algorithms (2001)
  4. Binder, Thomas; Blank, Luise; Bock, H.Georg; Bulirsch, Roland; Dahmen, Wolfgang; Diehl, Moritz; Kronseder, Thomas; Marquardt, Wolfgang; Schlöder, Johannes P.; von Stryk, Oskar: Introduction to model based optimization of chemical processes on moving horizons (2001)
  5. Großhans, Oliver: Optimal control of a reactive stagnation point flow on a catalytic plate (2001)
  6. Bock, H.G.; Diehl, M.M.; Leineweber, D.B.; Schlöder, J.P.: A direct multiple shooting method for real-time optimization of nonlinear DAE processes (2000)
  7. Gill, Philip E.; Jay, Laurent O.; Leonard, Michael W.; Petzold, Linda R.; Sharma, Vivek: An SQP method for the optimal control of large-scale dynamical systems (2000)
  8. Heinkenschloss, Matthias; Vicente, Luís N.: An interface between optimization and application for the numerical solution of optimal control problems (1999)
  9. Goldberg, Helmuth; Tröltzsch, Fredi: On a SQP-multigrid technique for nonlinear parabolic boundary control problems (1998)
  10. Leineweber, Daniel: Efficient reduced SQP methods for the optimization of chemical processes described by large sparse DAE models (1998)
  11. Petzold, Linda; Rosen, J.Ben; Gill, Philip E.; Jay, Laurent O.; Park, Kihong: Numerical optimal control of parabolic PDEs using DASOPT (1997)
  12. Lee, A.Y.: Neighboring extremals of dynamic optimization problems with path equality constraints (1988)