Affiliations: [a] UMI-LAFMIA 3175 CNRS, CINVESTAV-IPN (National Polytechnic Institute), Mexico City, Mexico
| [b] Departamento de Control Automático, CINVESTAV-IPN (National Polytechnic Institute), Mexico City, Mexico
Correspondence:
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Corresponding author. Wen Yu, Departamento de Control Automático, CINVESTAV-IPN (National Polytechnic Institute), Mexico City, Mexico. E-mail: [email protected].
Abstract: In order to assure the stability of Takagi-Sugeno (T-S) fuzzy systems, the linear matrix inequality (LMI) should be applied. However, the LMI method cannot be applied online, because its computational complexity. In this paper, the T-S fuzzy control is transformed into a time-varying system. By using Riccati differential equation (RDE) and a special optimal-like controller, the T-S fuzzy control can be applied online. We prove that the T-S fuzzy control is stable and the trajectory tracking error converges to a bounded zone. Since RDE can be solved online, the novel T-S fuzzy control is adaptive and more simple and effective than LMI-based methods. We apply successfully this online fuzzy control to an autonomous underwater vehicle.
