Tunable Input-to-State Safety with Input Constraints

TL;DR

This paper introduces a framework for integrating input constraints into tunable input-to-state safety (TISSf), ensuring safety and input compatibility through geometric characterization and control design, demonstrated on a cruise control system.

Contribution

It develops a geometric approach to incorporate input constraints into TISSf, providing verifiable conditions and an offline parameter selection method for safe control.

Findings

Guarantees input compatibility under various constraints.

Ensures recursive feasibility of safety filters.

Demonstrates effectiveness on a cruise control system.

Abstract

Tunable input-to-state safety (TISSf) generalizes the input-to-state safety (ISSf) framework by incorporating a tuning function that regulates safety conservatism while preserving robustness against perturbations. Despite its flexibility, the TISSf tuning function is often designed without explicitly incorporating actuator limits, which can lead to incompatibility with input constraints. To address this gap, this paper proposes a framework that integrates general compact input constraints into tuning function synthesis. Leveraging a geometric perspective, we characterize the TISSf condition as a state-dependent half-space constraint and derive a verifiable certificate for input compatibility using support functions. This characterization transforms the compatibility requirement into a design constraint on the tuning function, yielding a prescriptive lower bound that defines an admissible family of tunings under input constraints. These results are specialized to norm-bounded, polyhedral, and box constraints, yielding tractable control design conditions. We show that these conditions, combined with tuning function monotonicity, guarantee input compatibility and recursive feasibility of the resulting quadratic program (QP)-based safety filter. Furthermore, an offline parameter selection procedure using a covering-based sampling strategy ensures compatibility across the entire safe set via a linear program (LP). A connected cruise control (CCC) application demonstrates robust safety under TISSf while enforcing input constraints by design.