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Gradient-Based Stochastic Extremum Seeking for Multivariable Systems With Distinct Input Delays
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DOI：10.1109/tac.2026.3673189.png)
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Abstract
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This article addresses the design and analysis of a multivariable gradient-based stochastic extremum-seeking control method for multi-input systems with arbitrary input delays. The approach accommodates systems with distinct time delays across input channels. It achieves local exponential stability of the closed-loop system, guaranteeing convergence to a small neighborhood around the extremum point. By incorporating phase compensation for dither signals and a novel predictor–feedback mechanism with averaging-based estimates of the unknown gradient and Hessian, the proposed method overcomes traditional challenges associated with arbitrary, distinct input delays. Unlike previous work on deterministic multiparameter extremum-seeking with distinct input delays, this stability analysis is achieved without using backstepping transformations, simplifying the predictor design and enabling a more straightforward implementation. Specifically, the direct application of Artstein’s reduction approach yields delay- and system-dimension-independent convergence rates, thus enhancing its practical applicability. A numerical example and a source-seeking application illustrate the robust performance and advantages of the proposed delay-compensated stochastic extremum-seeking method.
Keywords:
Averaging in infinite dimensions
gradient methods
multiparameter optimization
predictor feedback
stochastic extremum seeking
time delays
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7
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1.3W
Citations:
6.7W
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