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Numerical Solution of Optimal Control Problems with Sparse SQP-Methods

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Georg Wimmer

    (University of the Federal Armed Forces Hamburg, Chair for Theory of Electrical Engineering and Computational Electromagnetics Helmut-Schmidt-University)

  • Thorsten Steinmetz

    (University of the Federal Armed Forces Hamburg, Chair for Theory of Electrical Engineering and Computational Electromagnetics Helmut-Schmidt-University)

  • Markus Clemens

    (University of the Federal Armed Forces Hamburg, Chair for Theory of Electrical Engineering and Computational Electromagnetics Helmut-Schmidt-University)

Abstract

Many physical processes can be modelled mathematically by ordinary differential equations. If such a process is governed by control variables an optimal control problem can be formulated. The basic problem is to choose the control variables such that some objective function is optimized while satisfying the differential equations. Approximating the control variables by linear functions and the state variables by low order Runge-Kutta schemes results in a nonlinear sparse constrained optimization problem. The inner iteration of a SQP-algorithm consists in solving an equality constrained quadratic optimization problem with a positive definite system matrix and a sparse constraint matrix. This optimization problem can be solved effectively by a projected cg-method when using a sparse LU decomposition of the constraint matrix.

Suggested Citation

  • Georg Wimmer & Thorsten Steinmetz & Markus Clemens, 2006. "Numerical Solution of Optimal Control Problems with Sparse SQP-Methods," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 996-1003, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_99
    DOI: 10.1007/978-3-540-34288-5_99
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