Title :
Maximum principle via singular perturbations
Author :
Gramme, Goetz P.
Author_Institution :
Inst. fur Inf. und Praktische Math., Kiel Univ., Germany
fDate :
6/21/1905 12:00:00 AM
Abstract :
The paper is concerned with necessary optimality conditions for parabolic boundary control problems. Its main purpose is to provide a regularization technique via singular perturbations to obtain optimality conditions for the time optimal control problem. The considered system is nonlinear and consists of a controlled coupled ODE/PDE. Systems of this type frequently arise in modelling population dynamics in a contaminated environment. For the regularization Ekeland´s variational principle along with a singular perturbation technique is used. For this purpose a new trajectory on an additional exterior domain, whose size may be considered as a singular perturbation parameter, is introduced. The technique allows us to obtain necessary optimality conditions without involving boundary data
Keywords :
distributed parameter systems; maximum principle; partial differential equations; singularly perturbed systems; time optimal control; variational techniques; Ekeland´s variational principle; necessary optimality conditions; parabolic boundary control problems; regularization technique; singular perturbations; Biological system modeling; Control systems; Couplings; Linear systems; Mathematical model; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear equations; Optimal control; Perturbation methods;
Conference_Titel :
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on
Print_ISBN :
0-7803-5250-5
DOI :
10.1109/CDC.1999.827792