Relationships Between Unscented and Sensitivity Function-Based Optimal Control for Space Flight

Abstract

Nearly all practical control problems in space engineering have uncertainty in system parameters creating the need for methods which can manage parametric uncertainty. Recently, open-loop optimal control has been proposed as a tool to manage uncertainties in the absence of feedback. Especially, unscented optimal control, which discretizes an uncertain optimal control problem into a deterministic problem, has been demonstrated as an efficient approach for problems with uncertain parameters/initial conditions. In this paper we study the performance of unscented optimal control methods using the concept of the sensitivity function. We show that the unscented optimal control formulation can capture the first and higher order effects introduced by parameter uncertainty. We also develop conditions under which the unscented discretion introduces no approximation errors in solving the continuous uncertain optimal control problems. The results shed new light on the unscented optimal control concept small-scale; and can be further explored to improve the efficiency in solving uncertain optimal control problems.