Dynamic neural observer with sliding mode learning

This paper deals with a state observation problem when the dynamic model of a plant contains an uncertainty or it is completely unknown (the only some smoothness properties are assumed to be in force). The dynamic neural network approach is applied in this informative situation. A new learning law, containing relay (signum) terms, is suggested to be in use. The nominal parameters of this procedure are adjusted during the preliminary "training process" where the sliding-mode technique as well as the LS-method are applied to obtain the "best" nominal parameter values using training experimental data. The upper bounds for the weights as well as for the averaged estimation error are derived. Two numeric examples illustrate this approach: first, the water ozone-purification process supplied by a bilinear model with unknown parameters, and, second, a nonlinear mechanical system, governed by the Euler's equations with unknown parameters and noises.