Compared to normal learning algorithms, for example backpropagation, the optimal bounded ellipsoid (OBE) algorithm has some better properties, such as faster convergence, since it has a similar structure as Kalman filter. OBE has some advantages over Kalman filter training, the noise is not required to be Guassian. In this paper OBE algorithm is applied in training the weights of the feedforward neural network for nonlinear system identification. Both hidden layers and output layers can be updated. From a dynamic system point of view, such training can be useful for all neural network applications requiring real-time updating of the weights. Two simulations give the effectiveness of the suggested algorithm.

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In this paper, we present a new sliding mode controller for a class of unknown nonlinear discrete-time systems. We make the following two modifications: 1) The neural identifier which is used to estimate the unknown nonlinear system, applies new learning algorithms. The stability and non-zero properties are proved by dead-zone and projection technique. 2) We propose a new sliding surface and give a necessary condition to assure exponential decrease of the sliding surface. The time-varying gain in the sliding mode produces a low-chattering control signal. The closed-loop system with sliding mode controller and neural identifier is proved to be stable by Lyapunov method.