1 results
Linearization techniques for $\mathbb{L}^{\infty}$
See PDF-control problemsand dynamic programming principles in classical and $\mathbb{L}^{\infty}$See PDF-control problems
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 18 / Issue 3 / July 2012
- Published online by Cambridge University Press:
- 17 August 2011, pp. 836-855
- Print publication:
- July 2012
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- Article
- Export citation
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The aim of the paper is to provide a linearization approach to the $\mathbb{L}^{\infty}$
-control problems. We begin by proving a semigroup-type behaviour of the set of constraints appearing in the linearized formulation of (standard) control problems. As a byproduct we obtain a linear formulation of the dynamic programming principle. Then, we use the $\mathbb{L}^{p}$
approach and the associated linear formulations. This seems to be the most appropriate tool for treating $\mathbb{L}^{\infty}$ problems in continuous and lower semicontinuous setting.
