Abstract
We consider a semilinear control system in a Banach space E. Relaxed (i.e. probability measure — valued) controls are introduced in a way that avoids special assumptions (such as compactness) on the control set, with a view to obtaining automatic existence theorems for optimal control problems. Relaxed trajectories are shown to be the same as those defined by differential inclusions. The set of relaxed trajectories is closed and results on optimal control of systems driven by ordinary controls are easily shown to generalize to the relaxed control setting.
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Fattorini, H.O. (1991). Relaxed controls in infinite dimensional systems. In: Desch, W., Kappel, F., Kunisch, K. (eds) Estimation and Control of Distributed Parameter Systems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 100. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6418-3_7
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DOI: https://doi.org/10.1007/978-3-0348-6418-3_7
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