Discrete approximation of nonconvex hyperbolic optimal control problems with state constraints
I. Chryssoverghi, Alex Bacopoulos, John Coletsos, B. Kokkinis · DSpace - NTUA (National Technical University of Athens) · 1998
We consider an optimal control problem for systems defined by nonlinear hyperbolic partial differential equations with state constraints. Since no convexity assumptions are made on the data, we also consider the control problem in relaxed form. We discretize both the classical and the relaxed problems by using a finite element method in space and a finite difference scheme in time, the controls being approximated by piecewise constant ones. We develop the existence theory and the necessary conditions for optimality, for the continuous and the discrete problems. Finally, we study the behaviour in the limit of discrete optimality, admissibility and extremality properties.