RT info:eu-repo/semantics/article
T1 Optimal Bounds for Numerical Approximations of Infinite Horizon Problems Based on Dynamic Programming Approach
A1 Frutos Baraja, Francisco Javier de
A1 Novo, Julia
K1 Matemáticas
K1 Análisis Numérico
K1 Dynamic programming
K1 Hamilton-Jacobi-Bellman equation
K1 optimal control
K1 error analysis
K1 1206 Análisis Numérico
K1 1207.05 Programación Dinámica
AB In this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach.It is well known that considering a time discretization with a positive step size $h$ an error bound of size $h$ can be proved for thedifference between the value function (viscosity solution of the Hamilton-Jacobi-Bellman equation corresponding to the infinite horizon) andthe value function of the discrete time problem. However, including also a spatial discretization based on elements of size $k$ an error bound of size $O(k/h)$ can be found in the literature for the error between the value functions of the continuous problem and the fully discrete problem. In this paper we revise the error bound of the fully discrete method and prove, under similar assumptions to those of the time discrete case, that the error of the fully discrete case is in fact $O(h+k)$ which gives first order in time and space for the method. This error bound matches the numerical experiments of many papers in the literature in which the behaviour $1/h$ from the bound $O(k/h)$ have not been observed.
PB SIAM
SN 0363-0129
YR 2023
FD 2023-04-30
LK https://uvadoc.uva.es/handle/10324/63850
UL https://uvadoc.uva.es/handle/10324/63850
LA spa
NO SIAM Journal on Control and Optimization, 61 (2023), 361-510
NO Producción Científica
DS UVaDOC
RD 11-jul-2024