Synthesis and Verification of Robust-Adaptive Safe Controllers for Uncertain Systems

Core Concepts

This work proposes the first verification and synthesis methods for adaptive-type safe controllers that can handle uncertain system dynamics. The key idea is to use robust-adaptive control barrier functions (raCBFs) to achieve safety guarantees for systems with unknown parameters.

Abstract

The paper presents a methodology for synthesizing and verifying robust-adaptive safe controllers for uncertain systems. The key contributions are:

Verification: The authors derive convex-equivalent conditions for an raCBF to provide safety guarantees. This allows them to pose raCBF verification as a sum-of-squares programming (SOSP) problem.

Synthesis: The authors design a multi-phase algorithm that synthesizes a valid raCBF with a locally optimal invariant set. The algorithm iteratively solves a sequence of SOSP problems to find the raCBF.

Experiments: The authors apply their algorithm to three examples with varying dynamics, dimensions (up to 7D), and safety specifications. They show that the synthesized raCBFs ensure 100% safety and provide up to 55% performance improvement over a robust baseline.

The key idea is to use robust-adaptive control, which combines the merits of robust and adaptive control. The raCBF depends on both the state and the estimated parameters, and it is paired with a parameter estimation law. This allows the controller to selectively apply conservatism when necessary, leading to better performance compared to a purely robust approach.

Stats

The paper does not contain any explicit numerical data or statistics. The key results are qualitative in nature, focusing on the safety and performance of the synthesized robust-adaptive controllers.

Quotes

"Our raCBFs are currently the most effective way to guarantee safety for uncertain systems, achieving 100% safety and up to 55% performance improvement over a robust baseline."

Key Insights Distilled From

Synthesis and verification of robust-adaptive safe controllers

by Simin Liu,Ka... at arxiv.org 04-04-2024

https://arxiv.org/pdf/2311.00822.pdf

Deeper Inquiries

How can the proposed synthesis algorithm be extended to handle time-varying unknown parameters

The proposed synthesis algorithm can be extended to handle time-varying unknown parameters by incorporating adaptive techniques into the parameter estimation process. Instead of assuming a constant parameter value, the algorithm can be modified to update the parameter estimate online based on the system's behavior. This adaptive parameter estimation can be integrated into the raCBF formulation, allowing the controller to adjust to changes in the unknown parameters over time. By continuously updating the parameter estimate, the raCBF can adapt to the evolving dynamics of the system, ensuring safety even in the presence of time-varying uncertainties.

What are the theoretical limitations of the robust-adaptive control barrier function approach, and how can they be addressed

Theoretical limitations of the robust-adaptive control barrier function approach include the complexity of handling high-dimensional systems and the computational burden associated with synthesizing and verifying the raCBFs. To address these limitations, advancements in optimization algorithms and computational tools can be leveraged to improve the efficiency of the synthesis process. Additionally, incorporating machine learning techniques for parameter estimation and adaptive control can enhance the robustness and adaptability of the raCBFs. By integrating state-of-the-art methods from control theory and optimization, the theoretical limitations of the approach can be mitigated, leading to more effective and scalable safety control solutions.

Can the ideas presented in this work be applied to other safety-critical control problems, such as those involving multi-agent systems or partially observable environments

The ideas presented in this work can be applied to other safety-critical control problems, such as those involving multi-agent systems or partially observable environments, with appropriate modifications and extensions. For multi-agent systems, the raCBF approach can be extended to coordinate the actions of multiple agents while ensuring safety constraints are met. By formulating collective safety objectives and synthesizing distributed raCBFs, the approach can be adapted to address the unique challenges of multi-agent coordination in complex environments.
In partially observable environments, the raCBF framework can be augmented with state estimation techniques, such as Kalman filters or particle filters, to account for uncertainty in the system's state information. By integrating observation models and estimation algorithms into the raCBF synthesis process, the controller can make decisions based on imperfect information while maintaining safety guarantees. Overall, the principles of robust-adaptive control barrier functions can be tailored to a wide range of safety-critical control problems, offering a versatile and robust framework for ensuring system safety in diverse scenarios.