Sub-optimal feedback control using a successive wavelet-Galerkin algorithm

We present a numerical algorithm for solving the Hamilton-Jacobi Bellman equation using a successive Galerkin-wavelet projection scheme. According to this scheme, the so-called generalized Hamilton-Jacobi-Bellman (GHJB) equation is solved iteratively starting from a stabilizing solution. As a basis function for the Galerkin projections we consider the anti-derivatives of the well-known Daubechies´ wavelets. Wavelets offer several advantages over traditional bases functions such as time-frequency localization and compact support. A numerical example illustrates the approach proposed.