A Multirate Variational Approach to Nonlinear MPC

TL;DR

This paper introduces a multirate nonlinear model predictive control strategy that leverages different timescales for system dynamics and control inputs, enabling larger prediction steps, computational savings, and recursive feasibility.

Contribution

It proposes a novel multirate formulation of NMPC using a variational model and tube-based linearization, enhancing efficiency and accuracy in nonlinear control systems.

Findings

Achieves computational savings compared to single-rate schemes.

Ensures recursive feasibility with larger time steps.

Demonstrates conservation properties and effectiveness through numerical examples.

Abstract

A multirate nonlinear model predictive control (NMPC) strategy is proposed for systems with dynamics and control inputs evolving on different timescales. The proposed multirate formulation of the system model and receding horizon optimal control problem allows larger time steps in the prediction horizon compared to single-rate schemes, providing computational savings while ensuring recursive feasibility. A multirate variational model is used with a tube-based successive linearization NMPC strategy. This allows either Jacobian linearization or linearization using quadratic and linear Taylor series approximations of the Lagrangian and generalized forces respectively, providing alternative means for computing linearization error bounds. The two approaches are shown to be equivalent for a specific choice of approximation points and their structure-preserving properties are investigated. Numerical examples are provided to illustrate the multirate approach, its conservation properties and computational savings.