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Nonlinear constrained optimal control problems as a rule suffer from the so-called two-norm discrepancy, which in particular says that under stable optimality conditions the objective functionals satisfy a quadratic local growth estimate in terms of the L 2 norms but in L ∞ neighborhoods of the solution only. Furthermore, in the case of weak local optima with continuous control functions, stability w.r.t. parameter changes usually can be expected to hold in L ∞ sense rather than in L p .

Stability and Local Growth Near Bounded-Strong Optimal Controls