MPC on manifolds with an application to the control of spacecraft attitude on SO(3)
For control theorists and practitioners, this work provides a theoretically grounded MPC method for systems on manifolds like SO(3), solving a known problem where continuous control laws fail.
The paper develops a model predictive control (MPC) framework for systems with discrete-time dynamics on smooth manifolds, preserving properties of conventional MPC. It demonstrates global asymptotic stability on manifolds with Euler characteristic ≠ 1, where continuous globally stabilizing control laws do not exist, and applies it to spacecraft attitude control on SO(3).
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.