Filters

2007 - 200912010 - 20111

More filters

20192
Reset filters

Settings

Author: Maurer, Helmut × Has files: Yes ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Optimal control problems with delays in state and control and mixed control-state constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Göllmann, Laurenz; Kern, Daniela; Maurer, Helmut
    Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control-state inequality constraints. Necessary optimality conditions in the form of Pontryagin's minimum principle are established. The proof proceeds by augmenting the delayed control problem to a nondelayed problem with mixed terminal boundary conditions to which Pontryagin's minimum principle is applicable. Discretization methods for the delayed control problem are discussed which amount to solving a large-scale nonlinear programming problem. It is shown that the Lagrange multipliers associated with the programming problem provide a consistent discretization of the advanced adjoint equation for the delayed control problem. An analytical example and two numerical examples from chemical engineering and economics illustrate the results.
  • Thumbnail Image
    Item
    Path planning and collision avoidance for robots : dedicated to Prof. Dr. Helmut Maurer on the occasion of his 65th birthday
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Gerdts, Matthias; Henrion, René; Hömberg, Dietmar; Landry, Chantal; Maurer, Helmut
    An optimal control problem to find the fastest collision-free trajectory of a robot surrounded by obstacles is presented. The collision avoidance is based on linear programming arguments and expressed as state constraints. The optimal control problem is solved with a sequential programming method. In order to decrease the number of unknowns and constraints a backface culling active set strategy is added to the resolution technique.