TY - JOUR
T1 - Takagi-Sugeno Dynamic Neuro-Fuzzy Controller of Uncertain Nonlinear Systems
AU - Cervantes, Jorge
AU - Yu, Wen
AU - Salazar, Sergio
AU - Chairez, Isaac
N1 - Publisher Copyright:
© 1993-2012 IEEE.
PY - 2017/12
Y1 - 2017/12
N2 - The identification problem incorporated in feedback control of uncertain nonlinear systems exhibiting complex behavior has been solved in different ways. Some of these solutions have used artificial intelligence methods like fuzzy logic and neural networks. However, their individual implementation suffers from certain drawbacks, such as the black-box nature of neural network and the problem of finding suitable membership functions for fuzzy systems. These weaknesses can be avoided by implementing a hybrid structure combining these two approaches, the so-called neuro-fuzzy system. In this paper, a neuro-fuzzy system that implements differential neural networks (DNNs) as consequences of Takagi-Sugeno (T-S) fuzzy inference rules is proposed. The DNNs substitute the local linear systems that are used in the common T-S method. In this paper, DNNs are used to provide an effective instrument for dealing with the identification of the uncertain nonlinear system, while the T-S rules are used to provide the framework of previous knowledge of the system. The main idea is to carry out an online identification process of an uncertain nonlinear system with the aim to design a closed-loop trajectory tracking controller. The methodology developed in this study that supports the identification and trajectory control designs is based on the Lyapunov formalism. The DNN implementation results in a time-varying T-S system. As a consequence, the solution of two time-varying Riccati equations was used to adjust the learning laws in the DNN as well as to adjust the gains of the controller. Two results were provided to justify the existence of positive-definite solutions for the class of Riccati equations used in the learning laws of DNNs. A complete description of the learning laws used for the set of DNN identifiers is also obtained. An autonomous underwater vehicle system is used to demonstrate the performance of the controller on tracking a desired 3-D path by this combination of the DNN and the T-S system.
AB - The identification problem incorporated in feedback control of uncertain nonlinear systems exhibiting complex behavior has been solved in different ways. Some of these solutions have used artificial intelligence methods like fuzzy logic and neural networks. However, their individual implementation suffers from certain drawbacks, such as the black-box nature of neural network and the problem of finding suitable membership functions for fuzzy systems. These weaknesses can be avoided by implementing a hybrid structure combining these two approaches, the so-called neuro-fuzzy system. In this paper, a neuro-fuzzy system that implements differential neural networks (DNNs) as consequences of Takagi-Sugeno (T-S) fuzzy inference rules is proposed. The DNNs substitute the local linear systems that are used in the common T-S method. In this paper, DNNs are used to provide an effective instrument for dealing with the identification of the uncertain nonlinear system, while the T-S rules are used to provide the framework of previous knowledge of the system. The main idea is to carry out an online identification process of an uncertain nonlinear system with the aim to design a closed-loop trajectory tracking controller. The methodology developed in this study that supports the identification and trajectory control designs is based on the Lyapunov formalism. The DNN implementation results in a time-varying T-S system. As a consequence, the solution of two time-varying Riccati equations was used to adjust the learning laws in the DNN as well as to adjust the gains of the controller. Two results were provided to justify the existence of positive-definite solutions for the class of Riccati equations used in the learning laws of DNNs. A complete description of the learning laws used for the set of DNN identifiers is also obtained. An autonomous underwater vehicle system is used to demonstrate the performance of the controller on tracking a desired 3-D path by this combination of the DNN and the T-S system.
KW - Autonomous underwater vehicle
KW - Takagi-Sugeno (T-S) fuzzy systems
KW - dynamic neural networks (DNNs)
KW - neuro-fuzzy systems
KW - trajectory tracking problem
UR - http://www.scopus.com/inward/record.url?scp=85038829480&partnerID=8YFLogxK
U2 - 10.1109/TFUZZ.2016.2612697
DO - 10.1109/TFUZZ.2016.2612697
M3 - Artículo
SN - 1063-6706
VL - 25
SP - 1601
EP - 1615
JO - IEEE Transactions on Fuzzy Systems
JF - IEEE Transactions on Fuzzy Systems
IS - 6
M1 - 7574365
ER -