Adaptive Neural Control Design for Nonlinear Distributed Parameter Systems With Persistent Bounded Disturbances
In this paper, an adaptive neural network (NN) control with a guaranteed L infin -gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system...
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| Vydáno v: | IEEE transactions on neural networks Ročník 20; číslo 10; s. 1630 - 1644 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York, NY
IEEE
01.10.2009
Institute of Electrical and Electronics Engineers |
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| ISSN: | 1045-9227, 1941-0093, 1941-0093 |
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| Abstract | In this paper, an adaptive neural network (NN) control with a guaranteed L infin -gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L infin -gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L infin -gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L infin -gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L infin -gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller. |
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| AbstractList | In this paper, an adaptive neural network (NN) control with a guaranteed L(infinity)-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L(infinity)-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L(infinity)-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L(infinity)-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L(infinity)-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller.In this paper, an adaptive neural network (NN) control with a guaranteed L(infinity)-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L(infinity)-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L(infinity)-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L(infinity)-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L(infinity)-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller. In this paper, an adaptive neural network (NN) control with a guaranteed {cal L}_{infty}-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an {cal L}_{infty}-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive {cal L}_{infty}-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the {cal L}_{infty}-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and {cal L}_{infty}-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller. In this paper, an adaptive neural network (NN) control with a guaranteed L infin -gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L infin -gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L infin -gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L infin -gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L infin -gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller. In this paper, an adaptive neural network (NN) control with a guaranteed L(infinity)-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L(infinity)-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L(infinity)-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L(infinity)-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L(infinity)-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller. In this paper, an adaptive neural network (NN) control with a guaranteed L sub(infin)-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L sub(infin)-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L sub(infin)-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L sub(infin)-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L sub(infin)-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller. |
| Author | Huai-Ning Wu Han-Xiong Li |
| Author_xml | – sequence: 1 givenname: Huai-Ning surname: WU fullname: WU, Huai-Ning organization: School of Automation Science and Electrical Engineering, Beihang University (formerly Beijing University of Aeronautics and Astronautics), Beijing, 100191, China – sequence: 2 givenname: Han-Xiong surname: LI fullname: LI, Han-Xiong organization: Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong-Kong |
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| Keywords | Differential equation Non linear control Lyapunov method Feedback regulation Control synthesis L Adaptive control Modeling Partial differential equation Optimization Control constraint Parabolic equation Linear matrix inequality neural network (NN) distributed parameter systems Distributed parameter system linear matrix inequality (LMI) Neural network Non linear system Closed feedback Radial basis function Galerkin-Petrov method Neurocontrollers Upper bound Input to state stability input-to-state stability (ISS) Distributed control Derivative gain control Galerkin method Temperature control Lyapunov function |
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| References | ge (ref22) 2001 jiang (ref31) 1998; 34 ref12 gahinet (ref10) 1995 ref30 ref33 ref32 ref2 ref1 christofides (ref14) 2001 ref17 ref16 ref19 ref18 khalil (ref21) 2002 curtain (ref11) 1995 ray (ref13) 1981 ioannou (ref34) 1996 sanner (ref24) 1991 ref23 ref26 ref25 ref20 el-farra (ref15) 2003; 39 ref28 ref27 ref29 ref8 ref7 ref9 ref4 ref3 ref6 ref5 |
| References_xml | – year: 1995 ident: ref10 publication-title: LMI control toolbox for use with MATLAB – ident: ref9 doi: 10.1137/1.9781611970777 – start-page: 2153 year: 1991 ident: ref24 article-title: gaussian networks for direct adaptive control publication-title: 1991 American Control Conference ACC doi: 10.23919/ACC.1991.4791778 – ident: ref7 doi: 10.1109/9.736066 – year: 2002 ident: ref21 publication-title: Nonlinear Systems – year: 1981 ident: ref13 publication-title: Advanced Process Control – ident: ref2 doi: 10.1109/9.159566 – ident: ref25 doi: 10.1109/9.486648 – ident: ref17 doi: 10.1109/TNN.2007.912592 – ident: ref1 doi: 10.1109/9.256331 – year: 2001 ident: ref22 publication-title: Stable Adaptive Neural Network Control – ident: ref19 doi: 10.1109/TCST.2005.847329 – ident: ref16 doi: 10.1109/TFUZZ.2007.896351 – ident: ref5 doi: 10.1109/TNN.2007.899159 – ident: ref23 doi: 10.1002/0471781819 – volume: 34 start-page: 825 year: 1998 ident: ref31 article-title: design of robust adaptive controllers for nonlinear systems with dynamic uncertainties publication-title: Automatica doi: 10.1016/S0005-1098(98)00018-1 – ident: ref12 doi: 10.1080/00207177908922716 – ident: ref27 doi: 10.1016/S0005-1098(01)00094-2 – ident: ref30 doi: 10.1016/j.automatica.2005.11.001 – ident: ref29 doi: 10.1109/TNN.2004.826130 – ident: ref20 doi: 10.1007/978-3-642-85949-6 – ident: ref26 doi: 10.1080/002071798222280 – year: 2001 ident: ref14 publication-title: Nonlinear and Robust Control of PDE Systems Methods and Applications to Transport-Reaction Processes doi: 10.1007/978-1-4612-0185-4 – ident: ref32 doi: 10.1109/9.256328 – ident: ref8 doi: 10.1016/j.fss.2006.09.014 – ident: ref6 doi: 10.1109/9.40769 – ident: ref18 doi: 10.1016/S0009-2509(01)00357-8 – year: 1996 ident: ref34 publication-title: Robust Adaptive Control – ident: ref28 doi: 10.1109/TAC.2003.811250 – ident: ref3 doi: 10.1109/9.701109 – ident: ref33 doi: 10.1109/9.481517 – year: 1995 ident: ref11 publication-title: An Introduction to Infinite Dimensional Linear Systems Theory doi: 10.1007/978-1-4612-4224-6 – volume: 39 start-page: 715 year: 2003 ident: ref15 article-title: analysis and control of parabolic pde systems with input constraints publication-title: Automatica doi: 10.1016/S0005-1098(02)00304-7 – ident: ref4 doi: 10.1016/S0167-6911(02)00125-1 |
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| Snippet | In this paper, an adaptive neural network (NN) control with a guaranteed L infin -gain performance is proposed for a class of parabolic partial differential... In this paper, an adaptive neural network (NN) control with a guaranteed L(infinity)-gain performance is proposed for a class of parabolic partial differential... In this paper, an adaptive neural network (NN) control with a guaranteed {cal L}_{infty}-gain performance is proposed for a class of parabolic partial... In this paper, an adaptive neural network (NN) control with a guaranteed L sub(infin)-gain performance is proposed for a class of parabolic partial... |
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| SubjectTerms | Adaptative systems Adaptive control Adaptive systems Algorithms Applied sciences Artificial intelligence Computer science; control theory; systems Computer Simulation Connectionism. Neural networks Control design Control nonlinearities Control system analysis Control system synthesis Control systems Control theory. Systems Distributed parameter systems Exact sciences and technology Feedback input-to-state stability (ISS) linear matrix inequality (LMI) Models, Theoretical neural network (NN) Neural networks Neural Networks (Computer) Nonlinear control systems Nonlinear Dynamics Programmable control Temperature control {\cal L}_{\infty} -gain control |
| Title | Adaptive Neural Control Design for Nonlinear Distributed Parameter Systems With Persistent Bounded Disturbances |
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