Über Normminimale Steuerungen von L-Prozessen und Lineare Optimierung bei Normbeschränkten Steuerungen

This paper is devoted to two problems in the theory of optimal control for linear processes. The first one is characterized by a cost of the form ess sup {p(u(t)):t∈a, b]}, whereby p denotes the distance function of a compact convex set C ° ?^m containing the origin as an interior point and u:a, b] → ?^m represents the control. In the second problem the cost depends linear on the controls, which are limited by a bound for ess sup {p(u(t)):t∈a, b]}. There will be proved two duality theorems leading to a method for the construction of optimal controls in the case of a strict convex C. For linear processes defined by piecewise analytic functions these controls are piecewise continuous.