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| We consider an optimal control problem subject to a coupled system of nonlinear hyperbolic partial differential equations and ordinary differential equations. The partial differential equation is given by the Saint-Venant equations (shallow water equations), which are hyperbolic transport equations modelling the motion of a fluid. The Saint-Venant equations are strongly coupled to the equations of motion of a mechanical multibody system through boundary conditions and generalized force terms.
We discuss properties of the optimal control problem and employ a discretization scheme using a Lax-Friedrich scheme in space for its numerical solution. To this end a reduced optimization problem is derived and solved by a sequential quadratic programming method. For the computation of gradients an adjoint equation is being solved.
Numerical results for an optimal braking maneuver of a truck with a basin filled with a fluid are discussed. |
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