Deterministic drift counteraction optimal control and its application to satellite life extension

Abstract

The paper considers a class of optimal control problems for deterministic nonlinear discrete-time systems, where the objective is to maximize the total yield or time until the system exits a specified set. While algorithms such as value iteration or policy iteration may be used to solve the Bellman equation and find the optimal cost-to-go function and control policy, these algorithms may require a relatively large number of iterations to converge and the computational effort grows exponentially with the dimension of the system. This paper proposes a novel algorithm with the potential of achieving convergence of value iterations significantly faster. The new algorithm is based on adaptive proportional updates. This algorithm is applied to an optimal control problem of maximizing the lifetime of a satellite subject to J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and atmospheric drag perturbations.