On-line learning of dynamical systems in the presence of model mismatch and disturbances
This paper is concerned with the online learning of unknown dynamical systems using a recurrent neural network. The unknown dynamic systems to be learned are subject to disturbances and possibly unstable. The neural-network model used has a simple architecture with one layer of adaptive connection w...
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| Veröffentlicht in: | IEEE transactions on neural networks Jg. 11; H. 6; S. 1272 - 1283 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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IEEE
01.11.2000
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| ISSN: | 1045-9227 |
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| Abstract | This paper is concerned with the online learning of unknown dynamical systems using a recurrent neural network. The unknown dynamic systems to be learned are subject to disturbances and possibly unstable. The neural-network model used has a simple architecture with one layer of adaptive connection weights. Four learning rules are proposed for the cases where the system state is measurable in continuous or discrete time. Some of these learning rules extend the /spl sigma/-modification of the standard gradient learning rule. Convergence properties are given to show that the weight parameters of the recurrent neural network are bounded and the state estimation error converges exponentially to a bounded set, which depends on the modeling error and the disturbance bound. The effectiveness of the proposed learning rules for the recurrent neural network is demonstrated using an illustrative example of tracking a Brownian motion. |
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| AbstractList | This paper is concerned with the on-line learning of unknown dynamical systems using a recurrent neural network. The unknown dynamic systems to be learned are subject to disturbances and possibly unstable. The neural-network model used has a simple architecture with one layer of adaptive connection weights. Four learning rules are proposed for the cases where the system state is measurable in continuous or discrete time. Some of these learning rules extend the sigma-modification of the standard gradient learning rule. Convergence properties are given to show that the weight parameters of the recurrent neural network are bounded and the state estimation error converges exponentially to a bounded set, which depends on the modeling error and the disturbance bound. The effectiveness of the proposed learning rules for the recurrent neural network is demonstrated using an illustrative example of tracking a Brownian motion.This paper is concerned with the on-line learning of unknown dynamical systems using a recurrent neural network. The unknown dynamic systems to be learned are subject to disturbances and possibly unstable. The neural-network model used has a simple architecture with one layer of adaptive connection weights. Four learning rules are proposed for the cases where the system state is measurable in continuous or discrete time. Some of these learning rules extend the sigma-modification of the standard gradient learning rule. Convergence properties are given to show that the weight parameters of the recurrent neural network are bounded and the state estimation error converges exponentially to a bounded set, which depends on the modeling error and the disturbance bound. The effectiveness of the proposed learning rules for the recurrent neural network is demonstrated using an illustrative example of tracking a Brownian motion. This paper is concerned with the on-line learning of unknown dynamical systems using a recurrent neural network. The unknown dynamic systems to be learned are subject to disturbances and possibly unstable. The neural-network model used has a simple architecture with one layer of adaptive connection weights. Four learning rules are proposed for the cases where the system state is measurable in continuous or discrete time. Some of these learning rules extend the sigma-modification of the standard gradient learning rule. Convergence properties are given to show that the weight parameters of the recurrent neural network are bounded and the state estimation error converges exponentially to a bounded set, which depends on the modeling error and the disturbance bound. The effectiveness of the proposed learning rules for the recurrent neural network is demonstrated using an illustrative example of tracking a Brownian motion. This paper is concerned with the online learning of unknown dynamical systems using a recurrent neural network. The unknown dynamic systems to be learned are subject to disturbances and possibly unstable. The neural-network model used has a simple architecture with one layer of adaptive connection weights. Four learning rules are proposed for the cases where the system state is measurable in continuous or discrete time. Some of these learning rules extend the /spl sigma/-modification of the standard gradient learning rule. Convergence properties are given to show that the weight parameters of the recurrent neural network are bounded and the state estimation error converges exponentially to a bounded set, which depends on the modeling error and the disturbance bound. The effectiveness of the proposed learning rules for the recurrent neural network is demonstrated using an illustrative example of tracking a Brownian motion. This paper is concerned with the online learning of unknown dynamical systems using a recurrent neural network. The unknown dynamic systems to be learned are subject to disturbances and possibly unstable. The neural-network model used has a simple architecture with one layer of adaptive connection weights. Four learning rules are proposed for the cases where the system state is measurable in continuous or discrete time. Some of these learning rules extend the sigma -modification of the standard gradient learning rule. Convergence properties are given to show that the weight parameters of the recurrent neural network are bounded and the state estimation error converges exponentially to a bounded set, which depends on the modeling error and the disturbance bound. The effectiveness of the proposed learning rules for the recurrent neural network is demonstrated using an illustrative example of tracking a Brownian motion. |
| Author | Jun Wang Danchi Jiang |
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| References | Krstic (13) 1995 12 15 Williams (6) 1989; 1 Rumelhart (4) 1986 Haykin (16) 1994 Cichocki (17) 1993 Kailath (18) 1980 2 3 Cybenko (1) 1989; 2 Narendra (14) 1989 5 7 8 9 Ljung (11) 1996 Pineda (10) 1995 |
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| SubjectTerms | Artificial neural networks Backpropagation algorithms Computer networks Convergence Cost function Disturbances Dynamical systems Dynamics Errors Function approximation Intelligent networks Learning Multi-layer neural network Neural networks On-line systems Recurrent neural networks |
| Title | On-line learning of dynamical systems in the presence of model mismatch and disturbances |
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