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arXiv · 2409.19352

Analytical Construction of CBF-Based Safety Filters for Simultaneous State and Input Constraints (Extended Version)

Peter A. Fisher·Anuradha M. Annaswamy
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Abstract

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.

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Peter A. Fisher, Anuradha M. Annaswamy. 2024-09-28. Analytical Construction of CBF-Based Safety Filters for Simultaneous State and Input Constraints (Extended Version). https://arxiv.org/abs/2409.19352

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