Compactness of a fixpoint set and optimal control

Abstract

Solutions of the dynamic equations in distributed parameter systems are usually obtained as fixpoints of suitable maps, as in Picard iteration. In optimal control of distributed parameter systems, some compactness of the fixpoint set is then needed to extract a convergent minimizing sequence. Two results are obtained to show, when the family of maps is equicontractive, that one can extract such a sequence under suitable hypotheses.

Keywords:

• contraction mapping principle
• fixpoint set
• compactness
• optimal control
• distributed parameter systems
• constrained control