Novel cascade spline architectures for the identification of nonlinear systems

In this paper two novel nonlinear cascade adaptive architectures, here called sandwich models, suitable for the identification of general nonlinear systems are presented. The proposed architectures rely on the combination of structural blocks, each one implementing a linear filter or a memoryless nonlinear function. All the nonlinear functions involved in the adaptation process are based on spline functions and can be easily modified during learning using gradient-based techniques. In particular, a simple form of the on-line adaptation algorithms for the two architectures is derived. In addition, we analytically obtain a bound for the selection of the learning rates involved in the learning algorithms, in order to guarantee a convergence towards a minimum of the cost function. Finally, some experimental results demonstrate the effectiveness of the proposed method.