Input-to-State Safe Backstepping: Robust Safety-Critical Control with Unmatched Uncertainties
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910010519322624 |
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| author | Cohen, Max H. Ong, Pio Ames, Aaron D. |
| author_facet | Cohen, Max H. Ong, Pio Ames, Aaron D. |
| contents | Guaranteeing safety in the presence of unmatched disturbances -- uncertainties that cannot be directly canceled by the control input -- remains a key challenge in nonlinear control. This paper presents a constructive approach to safety-critical control of nonlinear systems with unmatched disturbances. We first present a generalization of the input-to-state safety (ISSf) framework for systems with these uncertainties using the recently developed notion of an Optimal Decay CBF, which provides more flexibility for satisfying the associated Lyapunov-like conditions for safety. From there, we outline a procedure for constructing ISSf-CBFs for two relevant classes of systems with unmatched uncertainties: i) strict-feedback systems; ii) dual-relative-degree systems, which are similar to differentially flat systems. Our theoretical results are illustrated via numerical simulations of an inverted pendulum and planar quadrotor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03691 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Input-to-State Safe Backstepping: Robust Safety-Critical Control with Unmatched Uncertainties Cohen, Max H. Ong, Pio Ames, Aaron D. Systems and Control Robotics Optimization and Control Guaranteeing safety in the presence of unmatched disturbances -- uncertainties that cannot be directly canceled by the control input -- remains a key challenge in nonlinear control. This paper presents a constructive approach to safety-critical control of nonlinear systems with unmatched disturbances. We first present a generalization of the input-to-state safety (ISSf) framework for systems with these uncertainties using the recently developed notion of an Optimal Decay CBF, which provides more flexibility for satisfying the associated Lyapunov-like conditions for safety. From there, we outline a procedure for constructing ISSf-CBFs for two relevant classes of systems with unmatched uncertainties: i) strict-feedback systems; ii) dual-relative-degree systems, which are similar to differentially flat systems. Our theoretical results are illustrated via numerical simulations of an inverted pendulum and planar quadrotor. |
| title | Input-to-State Safe Backstepping: Robust Safety-Critical Control with Unmatched Uncertainties |
| topic | Systems and Control Robotics Optimization and Control |
| url | https://arxiv.org/abs/2602.03691 |