Thursday 20 March 2025
The quest for safety in autonomous systems has long been a pressing concern, as even the most advanced machines can’t always anticipate every possible scenario. To address this issue, researchers have turned to control barrier functions (CBFs), a technique that ensures a system stays within safe boundaries by checking for potential collisions and other hazards. Now, a new paper proposes an innovative approach to verifying and synthesizing these safety-critical CBFs using sums-of-squares (SOS) programming.
The authors of the study have developed a novel framework that leverages SOS programming to validate and design CBFs for high-order control systems. These advanced control systems involve complex interactions between multiple components, making it challenging to ensure their safety. By applying SOS programming, researchers can efficiently verify and synthesize CBFs that guarantee safe system behavior.
The method works by formulating SOS programs that check whether a given system satisfies the conditions required for safety. In essence, these programs test whether a system’s dynamics are guaranteed to remain within safe boundaries. The framework also includes a synthesis component that generates CBFs from scratch, ensuring that they meet specific safety requirements.
One of the key benefits of this approach is its ability to handle high-order control systems with ease. Traditional methods often struggle with such complex systems, as they can become computationally expensive or even intractable. SOS programming, on the other hand, provides a scalable and efficient solution for verifying and synthesizing CBFs.
The authors have demonstrated the effectiveness of their framework through numerical simulations involving a system with seven control barrier functions (CBFs) of maximum relative degree two. The results show that their approach successfully synthesizes all 14 class K functions required to ensure the safety of the system, providing a high level of assurance for safe autonomy.
This innovation has significant implications for the development of autonomous systems, particularly in areas where safety is paramount, such as robotics and self-driving vehicles. By verifying and synthesizing CBFs using SOS programming, researchers can design safer and more reliable control systems that minimize the risk of accidents or malfunctions.
In addition to its practical applications, this research also sheds light on the theoretical foundations of control barrier functions. The authors’ framework provides a new perspective on the relationship between CBFs and SOS programming, advancing our understanding of these critical safety tools.
As autonomous systems continue to play an increasingly important role in our daily lives, ensuring their safety is crucial for widespread adoption.
Cite this article: “Verifying and Synthesizing Control Barrier Functions for Safe Autonomous Systems”, The Science Archive, 2025.
Autonomous Systems, Control Barrier Functions, Sums-Of-Squares Programming, Safety, Verification, Synthesis, High-Order Control Systems, Robotics, Self-Driving Vehicles, Assurance.
