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Logarithmic Regret for Online Control
We study optimal regret bounds for control in linear dynamical systems u...
09/11/2019 ∙ by Naman Agarwal, et al. ∙
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Online Linear Quadratic Control
We study the problem of controlling linear time-invariant systems with k...
06/19/2018 ∙ by Alon Cohen, et al. ∙
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An Online Optimization Approach for Multi-Agent Tracking of Dynamic Parameters in the Presence of Adversarial Noise
This paper addresses tracking of a moving target in a multi-agent networ...
02/21/2017 ∙ by Shahin Shahrampour, et al. ∙
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Distributed Online Optimization in Dynamic Environments Using Mirror Descent
This work addresses decentralized online optimization in non-stationary ...
09/09/2016 ∙ by Shahin Shahrampour, et al. ∙
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Regret Minimization in Partially Observable Linear Quadratic Control
We study the problem of regret minimization in partially observable line...
01/31/2020 ∙ by Sahin Lale, et al. ∙
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On the convergence of discrete-time linear systems: A linear time-varying Mann iteration converges iff the operator is strictly pseudocontractive
We adopt an operator-theoretic perspective to study convergence of linea...
03/28/2018 ∙ by Giuseppe Belgioioso, et al. ∙
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Turnpike in optimal shape design
We introduce and study the turnpike property for time-varying shapes, wi...
12/05/2019 ∙ by Gontran Lance, et al. ∙
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Distributed Online Linear Quadratic Control for Linear Time-invariant Systems
09/29/2020 ∙ by Ting-Jui Chang, et al. ∙
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Classical linear quadratic (LQ) control centers around linear time-invariant (LTI) systems, where the control-state pairs introduce a quadratic cost with time-invariant parameters. Recent advancement in online optimization and control has provided novel tools to study LQ problems that are robust to time-varying cost parameters. Inspired by this line of research, we study the distributed online LQ problem for identical LTI systems. Consider a multi-agent network where each agent is modeled as an LTI system. The LTI systems are associated with decoupled, time-varying quadratic costs that are revealed sequentially. The goal of the network is to make the control sequence of all agents competitive to that of the best centralized policy in hindsight, captured by the notion of regret. We develop a distributed variant of the online LQ algorithm, which runs distributed online gradient descent with a projection to a semi-definite programming (SDP) to generate controllers. We establish a regret bound scaling as the square root of the finite time-horizon, implying that agents reach consensus as time grows. We further provide numerical experiments verifying our theoretical result.
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