Tackling performativity in discrete-time dynamical systems: An iterative refinement approach
Zhang, Heling
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https://hdl.handle.net/2142/121972
Description
Title
Tackling performativity in discrete-time dynamical systems: An iterative refinement approach
Author(s)
Zhang, Heling
Issue Date
2023-11-10
Director of Research (if dissertation) or Advisor (if thesis)
Dong, Roy
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Control
Robust Optimal Control
Iterative Methods
Discrete-time Dynamical Systems
Conformal Prediction
Language
eng
Abstract
In many real-world dynamical systems, obtaining precise prior knowledge about system noise remains a challenge. This uncertainty complicates traditional control strategies, such as stochastic and robust control, especially when the noise exhibits "performativity''--- an explicit dependence on control inputs. Addressing this challenge, this paper presents a novel iterative method tailored for such systems. Our approach finds the open-loop control law that minimizes the worst-case loss, given that the noise induced by this control lies in its $(1 - p)$-confidence set for a predetermined $p$. At each iteration, we harness conformal prediction techniques to empirically estimate the confidence set shaped by the preceding control law. These derived confidence sets offer empirical constraints on the system's noise, guiding a robust control design that targets worst-case loss minimization. Under specific regularity conditions, our method is shown to converge to a near-optimal open-loop control. While our focus is on open-loop controls, the adaptive, data-driven nature of our approach suggests its potential applicability across diverse scenarios and extensions.
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