This paper deals with the robust adaptive observer design for nonlinear dynamic systems that have an underlying multiple time-scales structure via different time-scales neural network. The Lyapunov function method is used to develop a novel stable updating law for the multi-time scales neural networks model and prove that the state error, output estimation error and the neural network weights errors are all uniformly ultimately bounded around the zero point during the entire learning process. Furthermore, passivity-based approach is used to derive the robust property of the proposed multi-time scales neural networks observer. Compared with the other nonlinear observers without considering the time scales, the proposed observer demonstrates faster convergence and more accurate properties. Two examples are presented confirming the validity of the above approach.
- Adaptive learning
- Multi-time scale neural networks
- Nonlinear observer
- Nonlinear systems