Nonlinear robust performance analysis using complex-step gradient approximation

In this paper, the complex-step method is applied in the setting of numerical optimisation problems involving dynamical systems modelled as nonlinear differential equations. The main advantage of the complex-step method for gradient approximation is that it entails no subtractive cancellation error, and therefore the truncation error can be made arbitrarily (to machine precision) small. The method is applied to two robust performance analysis problems. The accuracy and convergence rate of the solutions computed using the proposed approach are seen to be significantly better than those achieved using standard gradient approximation methods.