Input-to-State Safe Backstepping: Robust Safety-Critical Control with Unmatched Uncertainties

2026-02-03

AI Summary

This work addresses the challenge of ensuring safety in nonlinear systems subject to unmatched disturbances that cannot be directly canceled by control inputs. To this end, a unified safe control framework is proposed by integrating optimal decay control barrier functions (Optimal Decay CBF), input-to-state safety (ISSf) theory, and backstepping design. The approach establishes a general construction mechanism for ISSf-CBFs applicable to both strict-feedback and double-relative-degree systems, significantly extending the applicability of safety-critical control to systems with unmatched uncertainties. Numerical simulations on an inverted pendulum and a planar quadrotor demonstrate that the proposed method effectively guarantees system safety even under strong unmatched disturbances.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• unmatched uncertainties
• safety-critical control
• input-to-state safety
• nonlinear systems
• disturbances

Innovation

• Input-to-State Safety
• Unmatched Uncertainties
• Control Barrier Functions
• Strict-Feedback Systems
• Optimal Decay CBF