An Efficient Move Blocking Strategy for Multiple Shooting based Nonlinear Model Predictive Control

TL;DR

This paper introduces a computationally efficient move blocking strategy for multiple shooting NMPC that reduces problem size and exploits sparsity, enabling longer horizons and faster solutions without sacrificing accuracy.

Contribution

It develops a new move blocking scheme integrated into multiple shooting NMPC, along with a sparsity-exploiting condensing algorithm for improved computational efficiency.

Findings

Reduces computational complexity from quadratic to linear in discretization nodes.

Enables longer prediction horizons with active-set methods.

Maintains accuracy and constraint satisfaction in simulations.

Abstract

Move blocking (MB) is a widely used strategy to reduce the degrees of freedom of the Optimal Control Problem (OCP) arising in receding horizon control. The size of the OCP is reduced by forcing the input variables to be constant over multiple discretization steps. In this paper, we focus on developing computationally efficient MB schemes for multiple shooting based nonlinear model predictive control (NMPC). The degrees of freedom of the OCP is reduced by introducing MB in the shooting step, resulting in a smaller but sparse OCP. Therefore, the discretization accuracy and level of sparsity is maintained. A condensing algorithm that exploits the sparsity structure of the OCP is proposed, that allows to reduce the computation complexity of condensing from quadratic to linear in the number of discretization nodes. As a result, active-set methods with warm-start strategy can be efficiently employed, thus allowing the use of a longer prediction horizon. A detailed comparison between the proposed scheme and the nonuniform grid NMPC is given. Effectiveness of the algorithm in reducing computational burden while maintaining optimization accuracy and constraints fulfillment is shown by means of simulations with two different problems.