An efficient implementation of graph-based invariant set algorithm for constrained nonlinear dynamical systems

TL;DR

This paper introduces an optimized implementation of the graph-based invariant set algorithm for nonlinear systems, significantly enhancing computational efficiency through adaptive subdivision and parallelization techniques.

Contribution

The paper presents a novel, efficient implementation of the GIS algorithm, incorporating machine learning-driven adaptive subdivision and parallel processing to handle higher-dimensional systems.

Findings

Speed improved by approximately 8x due to adaptive subdivision.

Parallelization increased computational speed by about 3x.

Demonstrated effectiveness through numerical example comparisons.

Abstract

The graph-based invariant set (GIS) algorithm is a promising set-based technique for computing the largest (with respect to inclusion) control invariant set of general discrete-time nonlinear dynamical systems. However, like other invariant set algorithms for nonlinear systems, the GIS algorithm may require a lot of resources when computing the control invariant set. This limits its applicability to higher dimensional systems. In this work, we present an improved and efficient implementation of the GIS algorithm for general discrete-time controlled nonlinear systems. We first identify the bottlenecks through extensive analysis, and then provide remedial procedures to improve the implementation of the GIS algorithm. Specifically, we developed an adaptive subdivision scheme using a supervised machine learning-based algorithm to reduce the cell growth rate and parallelize the graph construction step. We extensively demonstrate the performance of the improved GIS algorithm using a numerical example and compare the result to that of the standard GIS algorithm. The results show that the adaptive subdivision and the parallelization improved the speed of the algorithm by about 8x and 3x respectively, that of the standard GIS algorithm.