Relation between relaxability and performance stability for optimal control problems governed by non-linear evolution equations

Abstract

We establish an equivalence between notions of relaxability and well-posedness (stability) in the sense of performance criterion convergence for a large class of non-linear control systems with state and control constraints. We thereby obtain some intermediate results of independent interest, such as existence and closure theorems for the relaxed system and a density result of the original trajectories into the set of relaxed ones. The example of a parabolic system is formulated in detail.