Continuation model predictive control on smooth manifolds

TL;DR

This paper extends continuation model predictive control to systems with states constrained on smooth manifolds, providing an algorithm for real-time implementation and demonstrating its effectiveness on a hemisphere example.

Contribution

The authors develop a novel extension of continuation MPC for implicit manifold constraints, enabling control of more complex nonlinear systems.

Findings

Effective numerical performance on a hemisphere test problem

Algorithm suitable for real-time control implementation

Extension applicable to a broad class of constrained nonlinear systems

Abstract

Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. Continuation MPC, suggested by T.~Ohtsuka in 2004, uses Krylov-Newton iterations. Continuation MPC is suitable for nonlinear problems and has been recently adopted for minimum time problems. We extend the continuation MPC approach to a case where the state is implicitly constrained to a smooth manifold. We propose an algorithm for on-line controller implementation and demonstrate its numerical effectiveness for a test problem on a hemisphere.