We revisit the problem explored in [1] of guaranteeing satisfaction of multiple simultaneous state constraints applied to a single-input, single-output plant consisting of a chain of n integrators subject to input limitations. For this problem setting, we derive an analytic, easy-to-implement safety filter which respects input limitations and ensures forward-invariance of all state constraints simultaneously. Additionally, we provide a straightforward extension to the multi-input, multi-output chained integrator setting, and provide an analytic safety filter guaranteeing satisfaction of arbitrarily many simultaneous hyperplane constraints on the output vector. Whereas the approach in [1] obtains maximal invariant sets, our approach trades off some degree of conservatism in exchange for a recursive safety filter which is analytic for any arbitrary n >= 1.
@article{arxiv.2409.19352,
title = {Analytical Construction of CBF-Based Safety Filters for Simultaneous State and Input Constraints (Extended Version)},
author = {Peter A. Fisher and Anuradha M. Annaswamy},
journal= {arXiv preprint arXiv:2409.19352},
year = {2024}
}