Non-rational Infinite-Horizon Control: A Unified Framework for Robust Control through Frequency-Domain Optimization

ABSTRACT: 
Infinite-horizon controllers provide scalable alternatives to finite-horizon designs with long-term performance and stability guarantees. However, synthesizing them is challenging due to their infinite-dimensional nature and the non-triviality of causality and other information constraints. In this talk, I will introduce a novel framework for scalable and efficient synthesis of a broad class of infinite-horizon control problems. This framework unifies several classical designs—such as H2/LQG, H∞, and regret-optimal control—and extends to advanced settings, including risk-sensitive, Wasserstein distributionally robust, Hp-norm, and mixed-criteria designs. By leveraging convex duality, the framework reformulates the original problem into a convex dual optimization over positive-definite operators, simplifying the incorporation of information constraints. It also enables efficient frequency-domain computation via variations of first-order methods such as projected gradient ascent and Frank-Wolfe. While the resulting controllers may have non-rational transfer functions, I will present a novel minimax rational approximation technique that yields near-optimal and stabilizing state-space controllers of any desired degree. I will conclude with numerical experiments demonstrating the framework’s effectiveness for distributional robust and mixed-criteria control.

BIOGRAPHY:
Taylan Kargin is a PhD candidate in Electrical Engineering at Caltech, advised by Prof. Babak Hassibi. His research lies at the intersection of control theory, optimization, and machine learning, with a focus on robust and adaptive control of dynamical systems under uncertainty. He earned his M.S. in Electrical Engineering from Caltech in 2023 and dual bachelor’s degrees in Electrical and Electronics Engineering and Physics from Bilkent University in 2019. As an undergraduate, he researched at the National Magnetic Resonance Research Center under the guidance of Prof. Tolga Çukur. Taylan also gained industry experience as an intern at Amazon, where he collaborated with Dr. Kevin Small on reinforcement learning for large language models.