Deterministic learning control of disturbed brunovsky systems

Deterministic learning control was investigated recently. Due to the existence of time varying disturbances, learning capability may be influenced. In this paper, deterministic learning theory is analyzed in environments with disturbances. With an appropriately designed neural adaptive controller, the disturbances are attenuated and partial persistent excitation (PE) condition for the radial basis neural network (RBF NN) is satisfied. By imposing uniform complete observability (UCO) technique, the tracking error and the neural weight estimate error exponentially converge to a neighborhood of zero in finite time and the size of the neighborhood relies not only on the amplitude of disturbances but also on the control gains. After the learning process, the estimated neural weights are stored in RBF NN and a constant neural controller can be implemented. The simulation shows the effectiveness of this scheme.