Pulse-Width Predictive Control for LTV Systems with Application to Spacecraft Rendezvous

TL;DR

This paper introduces a model predictive control method for linear time-varying systems with PWM, demonstrated on spacecraft rendezvous, combining explicit linearization and impulsive approximations for rapid solution convergence.

Contribution

It presents a novel MPC approach for LTV systems with PWM control, specifically tailored for spacecraft rendezvous, using explicit linearization and impulsive approximations for efficiency.

Findings

Effective in simulation for spacecraft rendezvous scenarios.

Rapid convergence due to explicit linearization and transition matrix use.

Handles linear time-varying plants with PWM control efficiently.

Abstract

This work presents a model predictive controller (MPC) that is able to handle linear time-varying (LTV) plants with PWM control. The MPC is based on a planner that employs a PAM or impulsive approximation as a hot-start and then uses explicit linearization around successive PWM solutions for rapidly improving the solution by means of linear programming. As an example, the problem of rendezvous of spacecraft for eccentric target orbits is considered. The problem is modeled by the LTV Tschauner-Hempel equations, whose transition matrix is explicit; this is exploited by the algorithm for rapid convergence. The efficacy of the method is shown in a simulation study.