Gradient Extremum Seeking With Nonconstant Delays
This paper proposes a gradient extremum seeking method to address locally quadratic static maps in the presence of time-varying delays. Accommodating nonconstant delays has a strong impact in the predictor construction in terms of the associated transport partial differential equation (PDE) with var...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9126769/ |
| _version_ | 1818616690202640384 |
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| author | George Carneiro Santos Tiago Roux Oliveira |
| author_facet | George Carneiro Santos Tiago Roux Oliveira |
| author_sort | George Carneiro Santos |
| collection | DOAJ |
| description | This paper proposes a gradient extremum seeking method to address locally quadratic static maps in the presence of time-varying delays. Accommodating nonconstant delays has a strong impact in the predictor construction in terms of the associated transport partial differential equation (PDE) with variable convection speeds beyond the restrictions imposed on the delay regarding its arbitrary duration but bounded variation. A novel predictor design using perturbation-based estimates of the unknown Gradient and Hessian of the map must be introduced to handle this variable nature of the delays, which can arise both in the input and output channels of the nonlinear map to be optimized. Local exponential stability and convergence to a small neighborhood of the unknown extremum point are guaranteed. This technical result is assured by using backstepping transformation and averaging theory in infinite dimensions. Implementation aspects of the presented predictor for variable delays as well as the extension to state-dependent delays are also discussed. At last, we introduce the first results in the topic of extremum seeking control for cascades of transport PDEs that are interconnected through boundary conditions. Such a PDE-PDE cascade is useful to represent simultaneous time- and state-dependent delays. A simulation example illustrates the effectiveness of the proposed predictor-based extremum seeking approach for time-delay compensation. |
| first_indexed | 2024-12-16T16:53:48Z |
| format | Article |
| id | doaj.art-a3914e6f7964487fa564137e6c5e806a |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T16:53:48Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-a3914e6f7964487fa564137e6c5e806a2022-12-21T22:23:57ZengIEEEIEEE Access2169-35362020-01-01812042912044610.1109/ACCESS.2020.30051869126769Gradient Extremum Seeking With Nonconstant DelaysGeorge Carneiro Santos0Tiago Roux Oliveira1https://orcid.org/0000-0002-2232-8715Department of Electronics and Telecommunication Engineering, State University of Rio de Janeiro (UERJ), Rio de Janeiro, BrazilDepartment of Electronics and Telecommunication Engineering, State University of Rio de Janeiro (UERJ), Rio de Janeiro, BrazilThis paper proposes a gradient extremum seeking method to address locally quadratic static maps in the presence of time-varying delays. Accommodating nonconstant delays has a strong impact in the predictor construction in terms of the associated transport partial differential equation (PDE) with variable convection speeds beyond the restrictions imposed on the delay regarding its arbitrary duration but bounded variation. A novel predictor design using perturbation-based estimates of the unknown Gradient and Hessian of the map must be introduced to handle this variable nature of the delays, which can arise both in the input and output channels of the nonlinear map to be optimized. Local exponential stability and convergence to a small neighborhood of the unknown extremum point are guaranteed. This technical result is assured by using backstepping transformation and averaging theory in infinite dimensions. Implementation aspects of the presented predictor for variable delays as well as the extension to state-dependent delays are also discussed. At last, we introduce the first results in the topic of extremum seeking control for cascades of transport PDEs that are interconnected through boundary conditions. Such a PDE-PDE cascade is useful to represent simultaneous time- and state-dependent delays. A simulation example illustrates the effectiveness of the proposed predictor-based extremum seeking approach for time-delay compensation.https://ieeexplore.ieee.org/document/9126769/Extremum seekingtime-varying delaysstate-dependent delayspredictor feedbackpartial differential equationsaveraging in infinite dimensions |
| spellingShingle | George Carneiro Santos Tiago Roux Oliveira Gradient Extremum Seeking With Nonconstant Delays IEEE Access Extremum seeking time-varying delays state-dependent delays predictor feedback partial differential equations averaging in infinite dimensions |
| title | Gradient Extremum Seeking With Nonconstant Delays |
| title_full | Gradient Extremum Seeking With Nonconstant Delays |
| title_fullStr | Gradient Extremum Seeking With Nonconstant Delays |
| title_full_unstemmed | Gradient Extremum Seeking With Nonconstant Delays |
| title_short | Gradient Extremum Seeking With Nonconstant Delays |
| title_sort | gradient extremum seeking with nonconstant delays |
| topic | Extremum seeking time-varying delays state-dependent delays predictor feedback partial differential equations averaging in infinite dimensions |
| url | https://ieeexplore.ieee.org/document/9126769/ |
| work_keys_str_mv | AT georgecarneirosantos gradientextremumseekingwithnonconstantdelays AT tiagorouxoliveira gradientextremumseekingwithnonconstantdelays |