A Data-Driven Krasovskii-Based Approach for Safety Controller Design of Time-Delayed Uncertain Polynomial Systems
Omid Akbarzadeh, MohammadHossein Ashoori, Amy Nejati, Abolfazl Lavaei
TL;DR
This work develops a data-driven framework to guarantee safety for discrete-time uncertain polynomial systems with unknown dynamics, disturbances, and time delays by extending control barrier certificates to Krasovskii functionals (RK-CBC). The method synthesizes RK-CBCs and robust safety controllers (R-SC) directly from finite input–state data via a sum-of-squares (SOS) optimization, reducing computational complexity relative to model-based delay formulations. The approach is validated on three case studies (Academic, Jet Engine Compressor, Spacecraft), demonstrating robust infinite-horizon safety under unknown disturbances and delays. The contributions enable safe operation of safety-critical cyber-physical systems without explicit system models, with practical implications for networked control and delayed-feedback scenarios.
Abstract
We develop a data-driven framework for the synthesis of robust Krasovskii control barrier certificates (RK-CBC) and corresponding robust safety controllers (R-SC) for discrete-time input-affine uncertain polynomial systems with unknown dynamics, while explicitly accounting for unknown-but-bounded disturbances and time-invariant delays using only observed input-state data. Although control barrier certificates have been extensively studied for safety analysis of control systems, existing work on unknown systems with time delays, particularly in the presence of disturbances, remains limited. The challenge of safety synthesis for such systems stems from two main factors: first, the system's mathematical model is unavailable; and second, the safety conditions should explicitly incorporate the effects of time delays on system evolution during the synthesis process, while remaining robust to unknown disturbances. To address these challenges, we develop a data-driven framework based on Krasovskii control barrier certificates, extending the classical CBC formulation for delay-free systems to explicitly account for time delays by aggregating delayed components within the barrier construction. The proposed framework relies solely on input-state data collected over a finite time horizon, enabling the direct synthesis of RK-CBC and R-SC from observed trajectories without requiring an explicit system model. The synthesis is cast as a data-driven sum-of-squares (SOS) optimization program, yielding a structured design methodology. As a result, robust safety is guaranteed in the presence of unknown disturbances and time delays over an infinite time horizon. The effectiveness of the proposed method is demonstrated through three case studies, including two physical systems.