Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions
In this work, substrate control of a biological process with unknown varying control gain, input saturation, and uncertain reaction rate is addressed. A novel adaptive controller is proposed, which tackles the combined effect of input saturation and unknown varying control gain with unknown upper an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/1/251 |
| _version_ | 1797543270053576704 |
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| author | Alejandro Rincón Fredy E. Hoyos John E. Candelo-Becerra |
| author_facet | Alejandro Rincón Fredy E. Hoyos John E. Candelo-Becerra |
| author_sort | Alejandro Rincón |
| collection | DOAJ |
| description | In this work, substrate control of a biological process with unknown varying control gain, input saturation, and uncertain reaction rate is addressed. A novel adaptive controller is proposed, which tackles the combined effect of input saturation and unknown varying control gain with unknown upper and lower bounds. The design is based on dead zone radially unbounded Lyapunov-like functions, with the state backstepping as control framework. The convergence of the modified tracking error and the boundedness of the updated parameters are ensured by means of the Barbalat’s lemma. As the first distinctive feature, a new second-order auxiliary system is proposed that tackles the effect of saturated input and the unknown varying control gain with unknown upper and lower bounds. As the second distinctive feature, the modified tracking error converges to a compact set whose width is user-defined, so that it does not depend on bounds of either external disturbances, model terms, or model coefficients. The convergence region of the current tracking error is determined for the closed loop system subject to the formulated controller and the proposed auxiliary system. Finally, numerical simulation illustrates the performance of the proposed controller. |
| first_indexed | 2024-03-10T13:42:11Z |
| format | Article |
| id | doaj.art-f5f4996f0ce9434c887ce7f790a28954 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T13:42:11Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-f5f4996f0ce9434c887ce7f790a289542023-11-21T02:58:07ZengMDPI AGApplied Sciences2076-34172020-12-0111125110.3390/app11010251Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov FunctionsAlejandro Rincón0Fredy E. Hoyos1John E. Candelo-Becerra2Grupo de Investigación en Desarrollos Tecnológicos y Ambientales—GIDTA, Facultad de Ingenieria y Arquitectura, Universidad Católica de Manizales, Carrera 23 No. 60-63, Manizales 170002, ColombiaFacultad de Ciencias, Escuela de Física, Universidad Nacional de Colombia, Sede Medellín, Carrera 65 No. 59A, 110, Medellín 050034, ColombiaDepartamento de Energía Eléctrica y Automática, Facultad de Minas, Universidad Nacional de Colombia, Sede Medellín, Carrera 80 No. 65-223, Robledo, Medellín 050041, ColombiaIn this work, substrate control of a biological process with unknown varying control gain, input saturation, and uncertain reaction rate is addressed. A novel adaptive controller is proposed, which tackles the combined effect of input saturation and unknown varying control gain with unknown upper and lower bounds. The design is based on dead zone radially unbounded Lyapunov-like functions, with the state backstepping as control framework. The convergence of the modified tracking error and the boundedness of the updated parameters are ensured by means of the Barbalat’s lemma. As the first distinctive feature, a new second-order auxiliary system is proposed that tackles the effect of saturated input and the unknown varying control gain with unknown upper and lower bounds. As the second distinctive feature, the modified tracking error converges to a compact set whose width is user-defined, so that it does not depend on bounds of either external disturbances, model terms, or model coefficients. The convergence region of the current tracking error is determined for the closed loop system subject to the formulated controller and the proposed auxiliary system. Finally, numerical simulation illustrates the performance of the proposed controller.https://www.mdpi.com/2076-3417/11/1/251input saturationuncertain nonlinear systemadaptive controlunknown control gainbackstepping controldead zone Lyapunov function |
| spellingShingle | Alejandro Rincón Fredy E. Hoyos John E. Candelo-Becerra Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions Applied Sciences input saturation uncertain nonlinear system adaptive control unknown control gain backstepping control dead zone Lyapunov function |
| title | Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions |
| title_full | Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions |
| title_fullStr | Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions |
| title_full_unstemmed | Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions |
| title_short | Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions |
| title_sort | adaptive control for a biological process under input saturation and unknown control gain via dead zone lyapunov functions |
| topic | input saturation uncertain nonlinear system adaptive control unknown control gain backstepping control dead zone Lyapunov function |
| url | https://www.mdpi.com/2076-3417/11/1/251 |
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