A solution of the time-optimal Hamilton-Jacobi-Bellman equation on the interval using wavelets

Wavelet basis functions allow efficient representation of functions with isolated singularities owing to their nice localization properties in both space/time and frequency domains. In this paper we propose a wavelet-extension algorithm (WEA) for solving the time-optimal Hamilton-Jacobi-Bellman (TO-HJB) equation using the Daubechies wavelets and their antiderivatives as weighting and trial functions, respectively. Convergence of the proposed numerical scheme is shown. The advantage of the proposed technique in the paper is demonstrated by numerical examples.