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A review from the PDE viewpoint of Hamilton-Jacobi-Bellman equations arising in optimal control with vectorial cost

Katzourakis, N. and Pryer, T. (2018) A review from the PDE viewpoint of Hamilton-Jacobi-Bellman equations arising in optimal control with vectorial cost. Journal of Nonlinear Functional Analysis, 2018. 6. ISSN 2052-532X

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To link to this item DOI: 10.23952/jnfa.2018.6

Abstract/Summary

This paper is a review of results on Optimisation which are perhaps not so standard in the PDE realm. To this end, we consider the problem of deriving the PDEs associated to the optimal control of a system of either ODEs or SDEs with respect to a \emph{vector-valued} cost functional. Optimisation is considered with respect to a partial ordering generated by a given cone. Since in the vector case minima may not exist, we define vectorial value functions as (Pareto) minimals of the ordering. Our main objective is the derivation of the model PDEs which turn out to be parametric families of HJB single equations instead of systems of PDEs. However, this allows the use of the theory of Viscosity Solutions.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:74871
Publisher:Mathematical Research Press

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