Robust Stability Analysis of Positive Lure System with Neural Network Feedback
It addresses robustness in uncertain nonlinear control systems, particularly with neural network components, representing an incremental advance in control theory.
This paper tackles the robustness analysis of Lur'e control systems with positivity constraints and neural network feedback, deriving an explicit formula for the stability radius and proposing a refinement method for neural network sector bounds.
This paper investigates the robustness of the Lur'e problem under positivity constraints, drawing on results from the positive Aizerman conjecture and robustness properties of Metzler matrices. Specifically, we consider a control system of Lur'e type in which not only the linear part includes parametric uncertainty but also the nonlinear sector bound is unknown. We investigate tools from positive linear systems to effectively solve the problems in complicated and uncertain nonlinear systems. By leveraging the positivity characteristic of the system, we derive an explicit formula for the stability radius of Lur'e systems. Furthermore, we extend our analysis to systems with neural network (NN) feedback loops. Building on this approach, we also propose a refinement method for sector bounds of NNs. This study introduces a scalable and efficient approach for robustness analysis of both Lur'e and NN-controlled systems. Finally, the proposed results are supported by illustrative examples.