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

Arthur Fleig, ,Chair of Serious Games, University of Bayreuth, 95440 Bayreuth, Germany, Lars Grüne, ,Chair of Applied Mathematics, University of Bayreuth, 95440 Bayreuth, Germany
2019 Mathematical Control and Related Fields  
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
more » ... to perform an in-depth analysis of strict dissipativity for different cost functions. 2020 Mathematics Subject Classification. Primary: 35Q84, 35Q93, 60G15; Secondary: 49N35, 93C15.
doi:10.3934/mcrf.2020053 fatcat:dmpc4sjvireh3n564szvyrkhxe