Online Optimization of Linear-Time Invariant Dynamical Systems with Cost Perception

Cothren, Liliaokeawawa; Ospina, Ana M.; Bianchin, Gianluca; Dall’Anese, Emiliano

doi:10.1109/ieeeconf56349.2022.10052021

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The Ss-ogd Algorithm1

Introduction1

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2023

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“…This is due to the greedy behavior of the update that does not take into account future dynamics. In this section, we propose a simple modification to this myopic OGD update (9), called SS-OGD that accounts for this shortcoming.…”

Section: The Ss-ogd Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Online Linear Quadratic Tracking With Regret Guarantees

Karapetyan,

Bolliger,

Tsiamis

et al. 2023

IEEE Control Syst. Lett.

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Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online optimization where the time-varying reference state is unknown a priori and is revealed after the applied control input. We show the equivalence of this problem to the control of linear systems subject to adversarial disturbances and propose a novel online gradient descent-based algorithm to achieve efficient tracking in finite time. We provide a dynamic regret upper bound scaling linearly with the path length of the reference trajectory and a numerical example to corroborate the theoretical guarantees.

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Section: The Ss-ogd Algorithmmentioning

confidence: 99%

“…Several recent works, e.g. [9], consider a similar setting with time-varying costs. These, however, are allowed to be estimated offline by training, incompatible with our setting, and without regret guarantees.…”

Section: Introductionmentioning

confidence: 99%