Issues of numerical accuracy and stability in inverse simulation

Inverse simulation algorithms based on integration have been widely applied to predict the control input time histories required for aircraft to follow ideally defined manoeuvres. Several different inverse simulation algorithms are available but these different methods are all subject to a number of numerical and stability problems, such as high frequency oscillation effects and also lower frequency oscillatory phenomena termed “constraint oscillations”. Difficulties can also arise in applications involving discontinuous manoeuvres, discontinuities within the model or input constraints involving actuator saturation. This paper has shown that the dynamic response properties of the internal system are the cause of the so-called “constraint oscillation” phenomenon. In addition, a new inverse simulation approach based on the constrained derivative-free Nelder–Mead search-based optimisation method has been developed to eliminate problems of discontinuities and saturation. Simulation studies involving nonlinear ship models suggest that this new approach leads to improved properties in terms of convergence and numerical stability.