Abstract
AbstractWe 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’.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference26 articles.
1. Achdou, Y., Camilli, F., Cutrì, A., Tchou, N.: Hamilton–Jacobi equations on networks. IFAC Proc. Vol. 44(1), 2577–2582 (2011)
2. Achdou, Y., Camilli, F., Cutrì, A., Tchou, N.: Hamilton–Jacobi equations constrained on networks. NoDEA Nonlinear Differ. Equ. Appl. 20(3), 413–445 (2013)
3. Achdou, Y., Oudet, S., Tchou, N.: Hamilton–Jacobi equations for optimal control on junctions and networks. ESAIM Control Optim. Calc. Var. 21(3), 876–899 (2015)
4. Bardi, M., Capuzzo-Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations. Systems and Control: Foundations and Applications. Birkhäuser Boston Inc., Boston (1997)
5. Barles, G.: Discontinuous viscosity solutions of first-order Hamilton–Jacobi equations: a guided visit. Nonlinear Anal. 20(9), 1123–1134 (1993)