Feedback spreading control laws for semilinear distributed parameter systems

Target control by using feedback spreading control with application to immunotherapy

“…This paper continues the search, started in (Kassara 2000), for the FSC laws and their applications. Its main contribution is to demonstrate that when a lower bound condition on the speed of the spread is satisfied, then an FSC law can be used in order that a target be reached by the state of a semi-linear distributed parameter system.…”

“…In (Kassara 2000), we show that the FSC laws can be built by making selections of a set-valued map which is expressed via tangential conditions as in the following way: for each couple ð y, zÞ 2 Z Â D let us consider the tangential condition, 8 > 0, 9 0 < h < and k pk such that, SðhÞz þ hð y þ pÞ 2 D and, !ðSðhÞz þ hð y þ pÞÞ ' !ðzÞ:…”

“…At the theoretical level, recent studies (Kassara 2000) investigate the problem of spreading control by a setvalued approach in the context of monotonicity with respect to a pre-order. They show that a suitable selection procedure of a tangential map involving both the map to be spread and the dynamics of the system may provide a feedback spreading control law termed in short by FSC law.…”

Feedback Spreading Control under Speed Constraints

“…The present study continues the investigation of the field as expounded in [13] by essentially concentrating on the speed of a spread. For this, we are motivated by the technical need to design spreads, taking into consideration both the speed and the time of spreading; cf.…”

“…Nevertheless, all of the approaches cited above have the disadvantage of being restricted to linear systems and concern only a few situations. In a recent study [13], it has been pointed out that feedback spreading controls for semilinear partial differential equations may be investigated in the framework of monotone solutions with respect to a preorder ; cf. [1,17].…”