MPC on manifolds with an application to the control of spacecraft attitude on SO(3)

TL;DR

This paper develops a model predictive control approach for systems on smooth manifolds, demonstrating its effectiveness in achieving global stability for spacecraft attitude control on SO(3), where continuous laws cannot suffice.

Contribution

It extends MPC design to systems on manifolds, preserving key properties and addressing the challenge of global stabilization with discontinuous control laws.

Findings

MPC preserves properties on manifolds similar to Euclidean spaces.

Discontinuous MPC laws can achieve global stability on manifolds with Euler characteristic not equal to 1.

Application to spacecraft attitude control on SO(3) demonstrates practical effectiveness.

Abstract

We develop a model predictive control (MPC) design for systems with discrete-time dynamics evolving on smooth manifolds. We show that the properties of conventional MPC for dynamics evolving on $\mathbb R^n$ are preserved and we develop a design procedure for achieving similar properties. We also demonstrate that for discrete-time dynamics on manifolds with Euler characteristic not equal to 1, there do not exist globally stabilizing, continuous control laws. The MPC law is able to achieve global asymptotic stability on these manifolds, because the MPC law may be discontinuous. We apply the method to spacecraft attitude control, where the spacecraft attitude evolves on the Lie group SO(3) and for which a continuous globally stabilizing control law does not exist. In this case, the MPC law is discontinuous and achieves global stability.