Computing controlled invariant sets of nonlinear control-affine systems

Scott Brown, Mohammad Khajenejad, Sze Zheng Yong and Sonia Martínez
Proceedings of the 62nd IEEE Int. Conf. on Decision and Control, Singapore, December 2023, to appear

Abstract:

In this paper, we consider the computation of controlled invariant sets (CIS) of discrete-time nonlinear control affine systems. We propose an iterative refinement procedure based on polytopic inclusion functions, which is able to approximate the maximal controlled invariant set to within a guaranteed precision. In particular, this procedure allows us to guarantee the invariance of the resulting near-maximal CIS while also computing sets of control inputs that enforce the invariance. Further, we propose an accelerated version of this procedure which refines the CIS by computing backward reachable sets of individual components of set unions, rather than all at once. This reduces the total number of iterations required for convergence, especially when compared with existing methods. Finally, we compare our methods to a sampling-based approach and demonstrate the improved accuracy and faster convergence.

File: main.pdf

Bib-tex entry:

@InProceedings{SB-MK-SY-SM:23-cdc,
author = {S. Brown and M. Khajenejad and S. Yong and S. Mart{\'\i}nez},
title = {Computing controlled invariant sets of nonlinear control-affine systems},
booktitle = {62nd IEEE Int. Conf. on Decision and Control},
pages = {},
year = {2023},
address = {Singapore, Singapore},
month = {December}
}