Lower Semicontinuous Solutions of Hamilton–Jacobi–Bellman Equations
Hélène Frankowska · SIAM Journal on Control and Optimization · 1993
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.