Abstract
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 ∘ ℝm containing the origin as an interior point and u:[a, b] → ℝm 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.
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Heindl, G. Über Normminimale Steuerungen von L-Prozessen und Lineare Optimierung bei Normbeschränkten Steuerungen. Manuscripta Math 9, 323–331 (1973). https://doi.org/10.1007/BF01343873
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DOI: https://doi.org/10.1007/BF01343873