By Takashi Tanaka (Purdue University)
Talk Abstract: Hypothesis testing problems lie at the core of the interface between control and information theory. In this talk, we will highlight several canonical CPS security challenges that require contributions from both the control and information theory communities.
We begin with a continuous-time “GPS spoofing game” to analyze the competition between an attacker, who tries to covertly misguide a vehicle into an unsafe region, and a detector, who tries to identify the attack based on the vehicle’s observed trajectory. Using Girsanov’s theorem and the generalized Neyman-Pearson lemma, we show that a constant bias injection attack as the attacker’s strategy and a likelihood ratio test as the detector’s strategy form the unique saddle point of the game. We also analyze the exponents of the type II error in the finite data length regime.
We then extend our analysis to covert attack synthesis and mitigation over nonlinear dynamics. By adopting Kullback–Leibler (KL) divergence as a stealthiness measure, we argue that the zero-sum game between the attacker and the controller can be naturally formulated as the so-called minimax KL control problem, which is closely related to the classically recognized risk-sensitive control problem and the nonlinear H-infinity control problem. While analytical solutions for saddle point strategies are generally unavailable, we show that a variational approach can be taken to compute them numerically. Specifically, we demonstrate how the path-integral control algorithm – a quantum-inspired, simulator-driven policy synthesis method – can approximate saddle-point policies for both players through Monte Carlo simulations.
Speaker Bio: Takashi Tanaka is an Associate Professor at the School of Aeronautics and Astronautics and the Elmore Family School of Electrical and Computer Engineering at Purdue University. He received his B.S. from the University of Tokyo and his M.S. and Ph.D. degrees in aerospace engineering from the University of Illinois at Urbana-Champaign. Dr. Tanaka was a Postdoctoral Associate with the Laboratory for Information and Decision Systems at the Massachusetts Institute of Technology from 2012 to 2015, and a postdoctoral researcher at KTH Royal Institute of Technology from 2015 to 2017. He was an Assistant Professor in the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin between 2017 and 2024, where he was an Associate Professor in 2024. Dr. Tanaka’s research interests include control theory and its applications, most recently the information-theoretic perspectives of optimal control problems. He received the DARPA Young Faculty Award, the AFOSR Young Investigator Program Award, and the NSF Career Award.