Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone
This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time r...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/471281 |
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| author | J. Humberto Pérez-Cruz José de Jesús Rubio E. Ruiz-Velázquez G. Solís-Perales |
| author_facet | J. Humberto Pérez-Cruz José de Jesús Rubio E. Ruiz-Velázquez G. Solís-Perales |
| author_sort | J. Humberto Pérez-Cruz |
| collection | DOAJ |
| description | This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term. |
| format | Article |
| id | doaj-art-9001d1cf76534ffdac5bef0cea57e4b8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9001d1cf76534ffdac5bef0cea57e4b82025-02-03T00:59:35ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/471281471281Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown DeadzoneJ. Humberto Pérez-Cruz0José de Jesús Rubio1E. Ruiz-Velázquez2G. Solís-Perales3Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Bulevar Marcelino García Barragán No. 1421, 44430 Guadalajara, JAL, MexicoSección de Estudios de Posgrado e Investigación, ESIME UA-IPN, Avenida de las Granjas No. 682, Colonia Santa Catarina, 02250 Mexico City, DF, MexicoCentro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Bulevar Marcelino García Barragán No. 1421, 44430 Guadalajara, JAL, MexicoCentro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Bulevar Marcelino García Barragán No. 1421, 44430 Guadalajara, JAL, MexicoThis paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.http://dx.doi.org/10.1155/2012/471281 |
| spellingShingle | J. Humberto Pérez-Cruz José de Jesús Rubio E. Ruiz-Velázquez G. Solís-Perales Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone Abstract and Applied Analysis |
| title | Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone |
| title_full | Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone |
| title_fullStr | Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone |
| title_full_unstemmed | Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone |
| title_short | Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone |
| title_sort | tracking control based on recurrent neural networks for nonlinear systems with multiple inputs and unknown deadzone |
| url | http://dx.doi.org/10.1155/2012/471281 |
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