Analytical Construction of CBF-Based Safety Filters for Simultaneous State and Input Constraints
<|reference_start|>Analytical Construction of CBF-Based Safety Filters for Simultaneous State and Input Constraints: 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.<|reference_end|>
@article{fisher2024analytical,
    title={Analytical Construction of CBF-Based Safety Filters for Simultaneous
  State and Input Constraints},
    author={Peter A. Fisher, Anuradha M. Annaswamy},
    journal={arXiv preprint arXiv:2409.19352},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.19352},
    primaryClass={eess.SY cs.SY}
}