An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation (Q1358131)

An adaptive grid scheme for the solution of the discrete first order Hamilton-Jacobi-Bellmann equation \[ \sup_{u\in U}\{v_h(x)-\beta v_h(\Phi_h(x,u))- hg(x,u)\}=0 \] on \(\Omega\subset \mathbb R^n\) with \(0<\beta<1\) is developed, where \(\Phi_h\) is the right hand side of a discrete time control system and \(g\) is the cost function. Error estimates are proved and an adapting iteration for the discretization of the state space is developed.