Convergence Properties of Fast quasi-LPV Model Predictive Control

TL;DR

This paper analyzes the convergence of an iterative algorithm for fast nonlinear model predictive control of quasi-linear parameter-varying systems, providing conditions for convergence, suboptimality, and an improved variant, with comparative benchmarks.

Contribution

It introduces new convergence conditions, a suboptimal solution approach, and an optimality-preserving variant for fast quasi-LPV model predictive control.

Findings

The algorithm converges under specified conditions.

The suboptimal variant offers a trade-off between speed and solution quality.

The proposed methods outperform a state-of-the-art solver in benchmarks.

Abstract

In this paper, we study the convergence properties of an iterative algorithm for fast nonlinear model predictive control of quasi-linear parameter-varying systems without inequality constraints. Compared to previous works considering this algorithm, we contribute conditions under which the iterations are guaranteed to converge. Furthermore, we show that the algorithm converges to suboptimal solutions and propose an optimality-preserving variant with moderately increased computational complexity. Finally, we compare both variants in terms of quality of solution and computational performance with a state-of-the-art solver for nonlinear model predictive control in two simulation benchmarks.