New sliding-mode learning law for dynamic neural network observer

This brief deals with a state observation problem when the dynamic model of a plant contains an uncertainty or it is completely unknown (only 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 least-squares 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 nonlinear third-order electrical system (Chua's circuit) with noises in the dynamics as well as in the output, and, second, the water ozone-purification process supplied by a bilinear model with unknown parameters.