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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01bk128d99j
Title: Online Control of Linear Time-Varying Dynamical Systems
Authors: Gradu, Paula
Advisors: Hazan, Elad
Department: Mathematics
Certificate Program: Applications of Computing Program
Class Year: 2021
Abstract: We consider the problem of online control of systems with linear time-varying dynamics. This is a general formulation that can be applied to control non-linear dynamical systems via local linearization. To cope with changing environments, we introduce the adaptive regret metric to the field of control. This metric, originally studied in online learning, measures performance in terms of regret vs. the best policy in hindsight on any interval in time, and thus captures the adaptation of the controller to changing dynamics. The three main contributions of this thesis are: (1) extension of previous literature to LTV systems, (2) for known dynamics, a novel efficient control meta-algorithm which converts a controller with poly-log regret bounds into one with a first-order adaptive regret bound, (3) for unknown dynamics, a novel efficient control algorithm which attains sublinear regret up to an unavoidable quantity which measures system variability. As a building block to our main results, we derive a meta algorithm with first-order adaptive regret for functions with memory, as well as an algorithm for estimation of changing linear operators, both of which may be of independent interest. We also validate our theoretical findings experimentally on (1) the canonical double integrator system under changing noise models, and (2) the non-linear inverted pendulum benchmark.
URI: http://arks.princeton.edu/ark:/88435/dsp01bk128d99j
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2021

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