Lower Semicontinuous Solutions of Hamilton–Jacobi–Bellman Equations
Author:
- Hélène FrankowskaHFHélène Frankowska
- 1 January 1993
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 31 (1) , 257-272
Abstract
The value function of Mayer’s problem arising in optimal control is investigated, and lower semicontinuous solutions of the associated Hamilton–Jacobi–Bellman equation are defined in three (equivalent) ways. Under quite weak assumptions about the control system, the value function is the unique solution. Moreover, it is stable with respect to perturbations of the control system and the cost. It coincides with the viscosity solution whenever it is continuous.Keywords
This publication has 18 references indexed in Scilit:
- Some Characterizations of Optimal Trajectories in Control TheorySIAM Journal on Control and Optimization, 1991
- Optimal control and semicontinuous viscosity solutionsProceedings of the American Mathematical Society, 1991
- A Survey of Viability TheorySIAM Journal on Control and Optimization, 1990
- Generalized viscosity solutions for Hamilton-Jacobi equations with time-measurable hamiltoniansJournal of Differential Equations, 1987
- On existence and uniqueness of solutions of Hamilton-Jacobi equationsNonlinear Analysis, 1986
- Differential Inclusions1984
- Some properties of viscosity solutions of Hamilton-Jacobi equationsTransactions of the American Mathematical Society, 1984
- Viscosity solutions of Hamilton-Jacobi equationsTransactions of the American Mathematical Society, 1983
- Convex Analysis and Measurable Multifunctions1977
- Deterministic and Stochastic Optimal Control1975