Chance Constrained Stochastic Optimal Control for Linear Systems with a Time Varying Random Control Matrix

TL;DR

This paper introduces a novel open-loop approach for solving chance constrained stochastic optimal control problems involving linear systems with time-varying random control matrices, focusing on joint chance constraints under specific assumptions.

Contribution

It reformulates joint chance constraints into biconvex constraints using Vysochanskij-Petunin inequality, enabling efficient solutions for complex stochastic control problems.

Findings

Method outperforms scenario approach in spacecraft rendezvous tasks.

Reformulation simplifies handling of joint chance constraints.

Applicable under moment and unimodality assumptions.

Abstract

This work proposes an open-loop methodology to solve chance constrained stochastic optimal control problems for linear systems with a stochastic control matrix. We consider a joint chance constraint for polytopic time-varying target sets under moment and unimodality assumptions. We reformulate the chance constraint into individual biconvex constraints using the one-sided Vysochanskij-Petunin inequality. We demonstrate our methodology on two spacecraft rendezvous problems. We compare the proposed method with the scenario approach and moment-based methods based on Cantelli's inequality.