A spline wavelet collocation method for the optimal control of flexible spacecraft

Abstract

A spline wavelet collocation method is presented to solve optimal control problem (OCP) of flexible spacecraft, which is often required to reorient and reposition with minimum manoeuvre time or fuel consumption. It is very difficult and computationally expensive to determine the open-loop optimal control inputs for flexible spacecraft, because the optimal control profile is often characterised by discontinuities or switching in the control variables. In our approach, the state and control variables are expanded via cubic spline wavelet decomposition, and then an OCP would be converted into a nonlinear programming problem where the wavelet coefficients are treated as the optimisation variables. As opposed to the usual pseudospectral method based on polynomial approximation, the wavelet advantageous properties of compact representation would inherently make it efficiently and accurately to solve nonlinear programming problem using standard solver. The novel approach is demonstrated by two typical optimal problems. The results show that our approach outperforms Gauss pseudospectral method for discontinuous OCPs arising from the flexible spacecraft.