Gradient-Based Stochastic Extremum-Seeking Control for Multivariable Systems with Distinct Input Delays
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| Format: | Preprint |
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2024
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| _version_ | 1866929593389154304 |
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| author | Silva, Paulo Cesar Souza Pellanda, Paulo Cesar Oliveira, Tiago Roux |
| author_facet | Silva, Paulo Cesar Souza Pellanda, Paulo Cesar Oliveira, Tiago Roux |
| contents | This paper 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 and 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 results in delay- and system-dimension-independent convergence rates, enhancing practical applicability. A numerical example illustrates the robust performance and advantages of the proposed delay-compensated stochastic extremum-seeking method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient-Based Stochastic Extremum-Seeking Control for Multivariable Systems with Distinct Input Delays Silva, Paulo Cesar Souza Pellanda, Paulo Cesar Oliveira, Tiago Roux Optimization and Control Systems and Control This paper 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 and 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 results in delay- and system-dimension-independent convergence rates, enhancing practical applicability. A numerical example illustrates the robust performance and advantages of the proposed delay-compensated stochastic extremum-seeking method. |
| title | Gradient-Based Stochastic Extremum-Seeking Control for Multivariable Systems with Distinct Input Delays |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2411.10580 |