Title: Exploiting structure in analysis and design of feedback systems with learning-based components
Abstract: Recent years have witnessed an increase in the deployment of learning algorithms for control and decision-making in autonomous systems. Despite their significant computational benefits, ensuring the safety and reliability of these learning-based components is challenging due to their large size and inherent nonlinearity. In this talk, we use non-Euclidean contraction theory and mixed monotone theory to develop a framework for the reachability analysis of dynamical systems. Using this framework, we certify the safety and robustness of systems with learning-based feedback controllers.
We start by studying the input-output behavior of a stand-alone implicit neural network. Implicit neural networks are a recently-developed class of learning algorithms that generalizes the structure of traditional neural networks by replacing their layers with a fixed-point equation. Using contraction theory, we study the solvability of their fixed-point equations and provide (i) tight conditions for their well-posedness, (ii) explicit bounds on their input-output reachable sets, and (iii) optimization problems for their robust training. We then consider the interconnection of a nonlinear dynamical system with a neural network feedback controller. Using a structure-preserving interval-based approach, we design an online compositional algorithm for the safety verification of the closed-loop system.
Biography: Saber Jafarpour is a postdoctoral research fellow in the School of Electrical and Computer Engineering at the Georgia Institute of Technology. Before that, he was a postdoctoral researcher at the Center for Control, Dynamical Systems, and Computation at the University of California, Santa Barbara. He received his Ph.D. from the Department of Mathematics and Statistics at Queen’s University in 2016. His research interests include stability analysis and control design for large-scale autonomous systems with applications to learning-enabled control systems, power grids, and transportation networks.
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