Lattice piecewise affine approximation of explicit model predictive control with application to satellite attitude control

TL;DR

This paper introduces a lattice PWA approximation method for explicit MPC in satellite attitude control, reducing online computation while maintaining performance, and proves system stability with simulation validation.

Contribution

It presents a novel lattice PWA approximation approach for explicit MPC, enabling efficient real-time control for complex satellite systems.

Findings

Achieves near-equivalent performance to linear MPC with lower online complexity

Proves asymptotic stability of the satellite control system under the approximation

Uses less fuel compared to LQR in simulations

Abstract

Satellite attitude cotrol is a crucial part of aerospace technology, and model predictive control(MPC) is one of the most promising controllers in this area, which will be less effective if real-time online optimization can not be achieved. Explicit MPC converts the online calculation into a table lookup process, however the solution is difficult to obtain if the system dimension is high or the constraints are complex. The lattice piecewise affine(PWA) function was used to represent the control law of explicit MPC, although the online calculation complexity is reduced, the offline calculation is still prohibitive for complex problems. In this paper, we use the sample points in the feasible region with their corresponding affine functions to construct the lattice PWA approximation of the optimal MPC controller designed for satellite attitude control. The asymptotic stability of satellite attitude control system under lattice PWA approximation has been proven, and simulations are executed to verify that the proposed method can achieve almost the same performance as linear online MPC with much lower online computational complexity and use less fuel than LQR method.