[Paper Review] Learning-Based Safety-Stability-Driven Control for Safety-Critical Systems under Model Uncertainties

Lei Zheng, Jiesen Pan+3 more|arXiv (Cornell University)|Aug 8, 2020

Advanced Control Systems Optimization20 references4 citations

TL;DR

This paper proposes a learning-based safety-stability-driven control (LBSC) framework for nonlinear safety-critical systems under model uncertainties. By using Gaussian Processes (GPs) to online estimate model error uncertainty bounds, LBSC formulates a quadratic program (QP) that jointly enforces safety via control barrier functions (CBFs), tracking stability via control Lyapunov functions (CLFs), and input constraints, achieving real-time, safe, and high-performance control in connected cruise control simulations with guaranteed safety and improved tracking accuracy.

ABSTRACT

Safety and tracking stability are crucial for safety-critical systems such as self-driving cars, autonomous mobile robots, industrial manipulators. To efficiently control safety-critical systems to ensure their safety and achieve tracking stability, accurate system dynamic models are usually required. However, accurate system models are not always available in practice. In this paper, a learning-based safety-stability-driven control (LBSC) algorithm is presented to guarantee the safety and tracking stability for nonlinear safety-critical systems subject to control input constraints under model uncertainties. Gaussian Processes (GPs) are employed to learn the model error between the nominal model and the actual system dynamics, and the estimated mean and variance of the model error are used to quantify a high-confidence uncertainty bound. Using this estimated uncertainty bound, a safety barrier constraint is devised to ensure safety, and a stability constraint is developed to achieve rapid and accurate tracking. Then the proposed LBSC method is formulated as a quadratic program incorporating the safety barrier, the stability constraint, and the control constraints. The effectiveness of the LBSC method is illustrated on the safety-critical connected cruise control (CCC) system simulator under model uncertainties.

Motivation & Objective

• To address the challenge of maintaining safety and tracking stability in safety-critical systems when accurate system models are unavailable.
• To mediate the tradeoff between safety guarantees and high-performance tracking under model uncertainties and control input constraints.
• To develop a learning-based control framework that dynamically adapts to unknown system dynamics using online uncertainty estimation.
• To ensure safety is never violated while maintaining rapid and accurate tracking performance in uncertain environments.
• To enable real-time applicability of safety-stability control for nonlinear systems with uncertain dynamics.

Proposed method

• Gaussian Processes (GPs) are used to learn and estimate the model error between the nominal system model and actual system dynamics in real time.
• The predicted mean and variance from GPs are used to construct a high-confidence uncertainty bound (D) for model errors.
• A safety barrier constraint is derived using zeroing control barrier functions (ZCBFs) based on the estimated uncertainty bound to ensure safety.
• A stability constraint is formulated using control Lyapunov functions (CLFs) to achieve rapid and accurate tracking performance.
• The LBSC controller is formulated as a constrained quadratic program (QP) that integrates the safety barrier, stability constraint, and control input constraints.
• The QP is solved online at 50 Hz, enabling real-time control with an average solution time of 2.45 ms per step.

Experimental results

Research questions

• RQ1 How can safety and tracking stability be simultaneously guaranteed in nonlinear safety-critical systems under model uncertainties?
• RQ2 Can Gaussian Processes effectively estimate model error uncertainty bounds in real time for control applications?
• RQ3 How can the tradeoff between safety and high-performance tracking be dynamically resolved when conflicts arise?
• RQ4 What is the performance of a learning-based control framework that integrates GP uncertainty estimation with CBF-CLF-QP formulations?
• RQ5 Can the proposed method achieve real-time control with guaranteed safety and improved tracking accuracy in uncertain dynamic environments?

Key findings

• The LBSC method successfully maintained the space headway between the autonomous vehicle and its front vehicle within the safe range of 25–100 meters under all simulation phases, even during sudden decelerations.
• The model errors in vehicle accelerations were consistently within the high-confidence uncertainty bounds estimated by GPs, validating the accuracy of the GP-based uncertainty estimation.
• The LBSC controller achieved faster convergence to the desired speed (20 m/s) than the GPAS method, with a lower tracking mean absolute error (MAE) across all phases.
• In phase 2, where the lead vehicle decelerated urgently, the LBSC method prioritized safety, resulting in a higher MAE but strict adherence to safety constraints, unlike the LBSC-N variant that violated safety.
• The LBSC controller generated smoother control inputs (wheel force) and velocity profiles compared to the GPAS method, indicating improved control robustness.
• The average QP solution time was 2.45 ms, and the total control latency per step was 9.8 ms, enabling real-time operation at 50 Hz control frequency.