Simple adaptive control using neural networks with offset error reduction for SISO nonlinear systems

This paper presents a simple adaptive control (SAC) using neural networks with offset error reduction for SISO nonlinear systems. This method aims for reducing the offset error caused by a parallel feedforward compensator (PFC) required to achieve the almost strictly positive real (ASPR) condition. The real plant together with the PFC will form an augmented plant that satisfies the ASPR condition. In this proposed method, the control input for the nonlinear plant is given by the sum of the output of a simple adaptive controller and the output of neural networks, while only a part of control input produced by SAC is fed to the PFC. The role of neural networks is to compensate the nonlinearities in the control system by using backpropagation learning algorithm. The role of simple adaptive controller is to perform the model matching for the linear system with unknown structures to a given linear reference model. Since only part of the SAC control input is fed to the PFC, the offset error will be reduced by the control system. Thus, both of the augmented plant output and the real plant output can follow significantly close to the output of the reference model. Finally, the effectiveness of this method is confirmed through computer simulations.