Distribution Steering for Discrete-Time Linear Systems with General Disturbances using Characteristic Functions

TL;DR

This paper introduces a novel method for controlling stochastic linear systems to reach desired distributions while satisfying chance constraints, using characteristic functions to handle distribution steering with disturbances.

Contribution

The paper presents a new distribution steering approach for discrete-time linear systems employing characteristic functions to manage general disturbances under chance constraints.

Findings

Effective distribution steering demonstrated on a 2D double-integrator.

Method handles various disturbances and initial conditions.

Shows promising results in controlling stochastic systems.

Abstract

We propose to solve a constrained distribution steering problem, i.e., steering a stochastic linear system from an initial distribution to some final, desired distribution subject to chance constraints. We do so by characterizing the cumulative distribution function in the chance constraints and by using the absolute distance between two probability density functions using the corresponding characteristic functions. We consider discrete-time, time-varying linear systems with affine feedback. We demonstrate the proposed approach on a 2D double-integrator perturbed by various disturbances and initial conditions.