Dispersion Sensitive Optimal Control: A Conditional Value-at-Risk-Based Tail Flattening Approach via Sequential Convex Programming

In this brief, we propose a sequential convex programming (SCP) framework for minimizing the terminal state dispersion of a stochastic dynamical system about a prescribed destination—an important property in high-risk contexts such as spacecraft landing. Our proposed approach seeks to minimize the conditional value-at-risk (CVaR) of the dispersion, thereby shifting the probability distribution away from the tails. This approach provides an optimization framework that is not overly conservative and can accurately capture more information about true distribution, compared with methods which consider only the expected value, or robust optimization methods. The main contribution of this brief is to present an approach that: 1) establishes an optimization problem with CVaR dispersion cost 2) approximated with one of the two novel surrogates which is then 3) solved using an efficient SCP algorithm. In 2), two approximation methods, a sampling approximation (SA) and a symmetric polytopic approximation (SPA), are introduced for transforming the stochastic objective function into a deterministic form. The accuracy of the SA increases with sample size at the cost of problem size and computation time. To overcome this, we introduce the SPA, which avoids sampling by using an alternative approximation and thus offers significant computational benefits. Monte Carlo simulations indicate that our proposed approaches minimize the CVaR of the dispersion successfully.

I. Introduction

This brief considers an optimal control problem of minimizing the terminal state dispersion of a stochastic dynamical system about a prescribed destination within a sequential convex programming (SCP) framework. This problem is mainly motivated by the precision landing of space vehicles [1], which serves as a representative example of high-risk situations where accuracy and reliability are of paramount importance. The achievement of accurate landings may potentially lead to a dramatic increase in the scientific returns from planetary exploration missions, which have historically been limited by landing accuracy, and also to a reduction in space travel costs through further development of reusable launch vehicles [2], [3].