A Framework for Time-Varying Optimization via Derivative Estimation

Optimization algorithms have a rich and funda-mental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time - typically in response to a dynamically changing environment - online optimization becomes a continuous-time trajectory...

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Bibliographic Details
Published in:	2024 European Control Conference (ECC) pp. 2730 - 2735
Main Authors:	Marchi, Matteo, Bunton, Jonathan, Silvestre, Joao Pedro, Tabuada, Paulo
Format:	Conference Proceeding
Language:	English
Published:	EUCA 25.06.2024
Subjects:	Cost function Estimation Europe Heuristic algorithms Ordinary differential equations Trajectory tracking Vectors
Online Access:	Get full text
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Summary:	Optimization algorithms have a rich and funda-mental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time - typically in response to a dynamically changing environment - online optimization becomes a continuous-time trajectory tracking problem. To accommodate these time vari-ations, one typically requires some inherent knowledge about their nature such as a time derivative. In this paper, we propose a novel construction and analysis of a continuous-time derivative estimation scheme based on "dirty-derivatives", and show how it naturally interfaces with continuous- time optimization algorithms using the language of ISS (Input-to-State Stability). More generally, we show how a simple Lyapunov redesign technique leads to provable sub optimality guarantees when composing this estimator with any well-behaved optimization algorithm for time-varying costs.
DOI:	10.23919/ECC64448.2024.10591302