SIAM Journal on Control and Optimization, Vol.35, No.4, 1422-1433, 1997
A Remark on Existence of Solutions of Infinite-Dimensional Noncompact Optimal-Control Problems
Without compactness of the semigroup, optimal controls for semilinear infinite dimensional central problems may not exist even under the usual convexity-lower semicontinuity assumptions, This is shown with two counterexamples, and two fixes for nonexistence are discussed.
Keywords:SYSTEMS