Tackling performativity in discrete-time dynamical systems: An iterative refinement approach

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Zhang, Heling

Contributors dc:contributor

• Dong, Roy

• Control
• Robust Optimal Control
• Iterative Methods
• Discrete-time Dynamical Systems
• Conformal Prediction

Statement dc:rights

• Copyright 2023 Heling Zhang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/121972

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F121972