An Adaptive Partial Sensitivity Updating Scheme for Fast Nonlinear Model Predictive Control

TL;DR

This paper introduces an adaptive sensitivity updating scheme for nonlinear model predictive control that selectively updates Jacobians based on system nonlinearity, reducing computational load while maintaining control accuracy.

Contribution

It proposes a novel partial Jacobian update method triggered by a curvature measure, enhancing efficiency in NMPC without sacrificing convergence guarantees.

Findings

Reduces computational time in NMPC by updating fewer sensitivities.

Maintains bounded error and convergence properties with the new scheme.

Demonstrates effectiveness through numerical simulations.

Abstract

In recent years, efficient optimization algorithms for Nonlinear Model Predictive Control (NMPC) have been proposed, that significantly reduce the on-line computational time. In particular, direct multiple shooting and Sequential Quadratic Programming (SQP) are used to efficiently solve Nonlinear Programming (NLP) problems arising from continuous-time NMPC applications. One of the computationally demanding steps for on-line optimization is the computation of sensitivities of the nonlinear dynamics at every sampling instant, especially for systems of large dimensions, strong stiffness, and when using long prediction horizons. In this paper, within the algorithmic framework of the Real-Time Iteration (RTI) scheme based on multiple shooting, an inexact sensitivity updating scheme is proposed, that performs a partial update of the Jacobian of the constraints in the NLP. Such update is triggered by using a Curvature-like Measure of Nonlinearity (CMoN), so that only sensitivities exhibiting highly nonlinear behaviour are updated, thus adapting to system operating conditions and possibly reducing the computational burden. An advanced tuning strategy for the updating scheme is provided to automatically determine the number of sensitivities being updated, with a guaranteed bounded error on the Quadratic Programming (QP) solution. Numerical and control performance of the scheme is evaluated by means of two simulation examples performed on a dedicated implementation. Local convergence analysis is also presented and a tunable convergence rate is proven, when applied to the SQP method.