Stability and sensitivity analysis for optimal control problems with control-state constraints
Volume 394 / 2001
Abstract
A family of parameter dependent optimal control problems (O)$_h$ with smooth data for nonlinear ODEs is considered. The problems are subject to pointwise mixed control-state constraints. It is assumed that, for a reference value $h_0$ of the parameter, a solution of (O)$_{h_0}$ exists. It is shown that if {(i)} {\it independence, controllability \rm and \it coercivity}\/ conditions are satisfied at the reference solution, then {(ii)} for each $h$ from a neighborhood of $h_0$, a locally unique solution to (O)$_h$ and the associated Lagrange multiplier exist, are Lipschitz continuous and Bouligand differentiable functions of the parameter. If, in addition, the dependence of the data on the parameter is {\it strong}, then {(ii)} implies {(i)}.
