Strict dissipativity analysis for classes of optimal control problems involving probability density functions

Titelangaben

Fleig, Arthur ; Grüne, Lars:
Strict dissipativity analysis for classes of optimal control problems involving probability density functions.
In: Mathematical Control and Related Fields. Bd. 11 (2021) Heft 4 . - S. 935-964.
ISSN 2156-8472
DOI: https://doi.org/10.3934/mcrf.2020053

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Abstract

Motivated by the stability and performance analysis of model predictive control schemes, we investigate strict dissipativity for a class of optimal control problems involving probability density functions. The dynamics are governed by a Fokker-Planck partial differential equation. However, for the particular classes under investigation involving linear dynamics, linear feedback laws, and Gaussian probability density functions, we are able to significantly simplify these dynamics. This enables us to perform an in-depth analysis of strict dissipativity for different cost functions.