A new radial basis function neural network based multi-variable adaptive pole-zero placement controller

In this paper a new multi-variable adaptive controller algorithm for non-linear dynamical systems has been derived which employs the Radial Basis Function (RBF) Neural Network. In the proposed controller, the unknown plant is represented by an equivalent model consisting of a linear time-varying sub-model plus a non-linear 'learning' sub-model. The parameters of the linear sub-model are identified by a recursive least squares (RLS) algorithm with a directional forgetting factor, whereas the unknown non-linear sub-model is modeled using the RBF neural network resulting in a new multi-variable non-linear controller with a generalized minimum variance performance index. In addition, the new controller overcomes the shortcomings of other linear control designs and provides an adaptive mechanism which ensures that both the closed-loop poles and zeros are placed at their pre-specified positions. Simulation results using a non-linear multi-input multi-output (MIMO) plant model demonstrate the effectiveness of the proposed controller.