Robust optimisation of low-thrust interplanetary transfers using evidence theory

This work presents the formulation and solution of optimal control problems under epistemic uncertainty, when this uncertainty is modelled with Dempster-Shaffer theory of evidence. The application is to the design of low-thrust interplanetary transfers when an epistemic uncertainty exists in the performance of the propulsion system and in the magnitude of the departure hyperbolic excess velocity. The problem is solved by transforming the exact formulation, that uses discontinuous Belief functions, into an inexact formulation that uses a new continuous statistical function, called S in the following, that approximates the value of the Belief function. The optimisation is realised by first building a surrogate model of the quantities of interest and associated S functions. The surrogate is then progressively updated as the optimisation proceeds. The proposed method is applied to the design of optimal low-thrust transfers from the Earth to asteroid Apophis.