The Fourier series interpolation method for the solution of the SDARE

In this paper, we propose the Fourier series interpolation (FSI) method for the solution of the SDARE* in which the state dependency of the coefficient matrices is of periodic nature. In particular, we focus on the SDAREs where the system matrix depends on a single state component in a periodic way. The main advantage of the FSI approach is that the Fourier coefficients are computed offline. This in turn results in significant reduction in online computations for the solution of the SDARE. The implementation and performance of the FSI method is explained by considering the dynamical positioning (DP) problem of a ship. This problem has been studied by using the SDARE controller and observer. This requires online computation of the solution of the SDAREs. We show that the FSI method significantly reduces the online computation time in comparison with the MATLAB routine “care” in a situation where online solution of the SDARE is required. The FSI method can be particularly useful in situations involving the systems having small time constants.