Control systems with delays: Areas of applications and present status of the linear theory

Vintage Capital in the AK Growth Model: A Dynamic Programming Approach - Extended version

“…Variants and improvements were proposed by Delfour [28], [26], [27], Vinter and Kwong [64], Delfour and Manitius [29], Ichikawa [47] (see also the references and the precise systematization of the argument in Chapter 4 of Bensoussan, Da Prato, Delfour and Mitter [13] [30] and Kolmanovskii and co-authors [54], [53], [55]. Kolmanovskii and co-authors have also given sufficient optimality conditions in term of the value function but they did not solve HJB equation except for the LQ case (without state or state/control constraints) and under suitable assumptions (see [54] ch.14 or [53] ch 6 or [55] ch.…”

“…We consider v as defined in Proposition II.2.11. It is easy to see from the first part of the proof that x φ (t) remain in Y as defined in (29) and so the Hamiltonian (as in the proof of Proposition II.2.11) can be expressed in the simplified form of equation (27). We introduce the function:…”