We prove an extension of the Superposition Principle by Ambrosio-Gigli-Savaré in the context of a control problem. In particular, we link the solutions of a finite-dimensional control system, with dynamics given by a differential inclusion, to a solution of a continuity equation in the space of probability measures with admissible vector field. We prove also a compactness and an approximation result for admissible trajectories in the space of probability measures.
CITATION STYLE
Cavagnari, G., Marigonda, A., & Piccoli, B. (2018). Superposition principle for differential inclusions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10665 LNCS, pp. 201–209). Springer Verlag. https://doi.org/10.1007/978-3-319-73441-5_21
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