EXISTENCE THEOREMS FOR OPTIMAL PROBLEMS WITH VECTOR VALUED COST FUNCTIONS.
BROWN UNIV PROVIDENCE R I CENTER FOR DYNAMICAL SYSTEMS
Pagination or Media Count:
The paper considers the following optimal control problem. Consider a control system 0.1 y dot ft,y,u where f maps J sub o X Y X E into Y, J sub o a sub o, b sub o is an interval, and Y,E are Euclidean spaces. By a solution of 0.1 is meant a triple J,y,u, where J included in J sub o is an interval, y J approaches Y is absolutely continuous, u J approaches E is Lebesgue measurable, and y dott ft,yt,ut, ut epsilon Ut,yt almost everywhere a.e. in J. The control domain U is a map from J sub o X Y into subsets of E.
- Operations Research