Approximate Quantiles for Stochastic Optimal Control of LTI Systems with Arbitrary Disturbances

TL;DR

This paper introduces a Taylor approximation-based method for efficiently computing quantile functions in stochastic LTI control, facilitating chance constraint handling in multi-vehicle planning under various disturbances.

Contribution

The paper presents a novel approach using Taylor approximations of quantile functions for stochastic control of LTI systems with arbitrary disturbances, enabling efficient chance constraint reformulation.

Findings

Effective in multi-satellite coordination scenarios

Handles Gaussian and Cauchy disturbances

Outperforms particle control in experiments

Abstract

We propose a method for open-loop stochastic optimal control of LTI systems based on Taylor approximations of quantile functions. This approach enables efficient computation of quantile functions that arise in chance constrained reformulations. We are motivated by multi-vehicle planning problems for LTI systems with norm-based collision avoidance constraints, and polytopic feasibility constraints. Respectively, these constraints can be posed as reverse-convex and convex chance constraints that are affine in the control and disturbance. We show for constraints of this form, piecewise affine approximations of the quantile function can be embedded in a difference-of-convex program that enables use of conic solvers. We demonstrate our method for multi-satellite coordination with Gaussian and Cauchy disturbances, and provide a comparison with particle control.