An adaptive wavelet collocation method for solving optimal control problem

Abstract

A sequential solution approach based on an adaptive wavelet collocation method is proposed for solving optimal control problems. By expanding the state and control variables with wavelet multi-resolution decomposition, an original optimal control problem can be transcribed into a nonlinear programming problem that can be solved by general methods. In the proposed framework, an iterative algorithm starts from an initial coarse grid with few collocations. Subsequent solutions can thus be obtained on a dynamically refined grid by an adaptive wavelet collocation method, while the previous coarser level solution can be taken as the initial guess for the next iteration. Consequently, the computational grid for direct numerical optimization method is able to automatically adapt to any irregularities or discontinuities in the solution. The efficiency and accuracy of the proposed algorithm are verified by two typical examples.