Complex-Step Gradient Approximation For Robustness Analysis of Nonlinear Systems
Abstract
In this paper, the complex-step perturbation method is extended to the setting of 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 subtraction cancellation error, and therefore the truncation error can be made arbitrarily small. The method is applied to two robust performance analysis problems and is shown to provide more accurate solutions and improved convergence times when compared with standard finite difference-based approaches.
