Time and Norm Optimality of Weakly Singular Controls [chapter]

H. O. Fattorini
2011 Parabolic Problems  
Letū(t) be a control that satisfies the infinite-dimensional version of Pontryagin's maximum principle for a linear control system, and let z(t) be the costate associated withū(t). It is known that integrability of z(t) in the control interval [0, T ] guarantees thatū(t) is time and norm optimal. However, there are examples where optimality holds (or does not hold) when z(t) is not integrable. This paper presents examples of both cases for a particular semigroup (the right translation semigroup
more » ... anslation semigroup in L 2 (0, ∞)). (2000) . 93E20, 93E25. Mathematics Subject Classification
doi:10.1007/978-3-0348-0075-4_12 fatcat:67bz6qht5vgcvdabztlqaage3q