Hamilton-Jacobi equations for optimal control on multidimensional junctions with entry costs

2019/03/20 by Manh-Khang Dao, Dao, Manh-Khang, Boualem Djehiche +1
Computer Science · #34H05 #35F21 #49J15 #49L20 #49L25 #93C30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1903.08400

openalex publication_date 2019/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that the value function of the optimal control problem is the unique viscosity solution of the HJ system. This is done under the usual strong controllability assumption and also under a weaker condition, coined 'moderate controllability assumption'.

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