Learning Piecewise Residuals of Control Barrier Functions for Safety of Switching Systems using Multi-Output Gaussian Processes

Core Concepts

Developing a safe learning-based control strategy for switching systems using batch multi-output Gaussian processes to mitigate uncertainty effects on Control Barrier Functions and Control Lyapunov Functions.

Abstract

The content introduces the concept of Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) for safety-critical control mechanisms in switching systems. It discusses the impact of model uncertainty on safety and stability guarantees, proposing a learning-based control strategy using multi-output Gaussian processes to approximate piecewise residuals. The feasibility of the resulting optimization is analyzed, and simulation results of a switching adaptive cruise control system validate the effectiveness of the proposed strategy.
I. Introduction

CBFs and CLFs ensure safety in hybrid dynamical systems.
Gaussian processes are used to approximate hybrid residual dynamics.
Recent focus on safety verification in control applications.
II. Problem Setup and Statement

Control-affine switching system model with state-dependent switching signal.
Definitions of Control Lyapunov Functions and Control Barrier Functions.
III. Proposed Batch MOGP-Based Design for Piecewise Residuals

Use of multi-output Gaussian processes to approximate piecewise residuals.
Conversion of uncertainty-aware chance constraints into second-order cone constraints.
IV. Simulation Results

Comparison of proposed MOGP-SOCP controller with baseline and nominal controllers.
Illustration of system trajectories, distance maintenance, and control inputs.
V. Conclusion

Development of a batch MOGP framework for uncertainty mitigation in safety-critical control mechanisms.

Stats

In [1], a GP is employed to learn the unmodeled dynamics for the safe navigation of quadrotors with CBFs.
In [1], a GP-based min-norm controller stabilizing an unknown control affine system using CLFs is introduced.
In [1], the effect of uncertainty on high-order CBFs is quantified using GPs.

Quotes

"CBFs have provided a powerful theoretical tool for synthesizing controllers that ensure the safety of dynamical systems."
"The resulting optimization is proven to be convex and can be solved in real-time."

Key Insights Distilled From

Learning Piecewise Residuals of Control Barrier Functions for Safety of Switching Systems using Multi-Output Gaussian Processes

by Mohammad Aal... at arxiv.org 03-28-2024

https://arxiv.org/pdf/2403.18041.pdf

Deeper Inquiries

What are the limitations of using Gaussian processes for approximating piecewise residuals in control systems

Using Gaussian processes for approximating piecewise residuals in control systems has some limitations. One limitation is the computational complexity associated with training the GP models, especially when dealing with high-dimensional systems or a large number of data samples. Additionally, GP models may struggle with capturing complex nonlinear relationships in the data, leading to inaccuracies in the approximation of piecewise residuals. Another limitation is the assumption of stationarity in the GP models, which may not hold true in dynamic systems where the underlying dynamics change over time. This can result in suboptimal performance and safety guarantees in control applications.

How can the proposed batch MOGP framework be extended to handle overlapping regions in switching systems

To extend the proposed batch MOGP framework to handle overlapping regions in switching systems, one approach could be to incorporate a more sophisticated data partitioning strategy. Instead of strictly non-overlapping regions, a clustering algorithm could be used to identify regions with similar dynamics and partition the data accordingly. This would allow the MOGP model to capture the transitions between overlapping regions and adapt to the changing dynamics more effectively. Additionally, the kernel functions in the MOGP model could be designed to account for the overlapping nature of the regions, enabling the model to learn the piecewise residuals in a more robust manner.

How might the integration of reinforcement learning techniques enhance the learning-based control strategy proposed in the article

The integration of reinforcement learning techniques could enhance the learning-based control strategy proposed in the article by introducing adaptive learning mechanisms. Reinforcement learning algorithms, such as deep Q-learning or policy gradient methods, could be used to optimize the control policy based on feedback from the system's performance. By incorporating reinforcement learning, the control strategy can adapt to changing environments, learn optimal control policies through trial and error, and improve decision-making in uncertain or dynamic scenarios. This adaptive learning approach could enhance the robustness and adaptability of the control system in real-world applications.