Non-parametric Identification of Homogeneous Dynamical Systems

The aim of this study is to design a non-parametric identifier for homogeneous systems based on a class of artificial neural networks with continuous dynamics. The identification algorithm is developed for input-affine systems with uncertain gains and diverse degrees of homogeneity. One of the main contributions of this study is the extension of the universal approximation property of neural networks for continuous homogeneous systems. Another contribution is the development of a differential non-parametric identifier based on the novel concept of homogeneous neural networks. The adjustment laws for the weights are obtained from a Lyapunov stability analysis taking homogeneity properties of the system into account. The ultimate boundedness of the origin for the identification error is demonstrated using the persistent excitation condition. The effectiveness of the proposed identifier is verified by the simulation of the three-tank homogeneous model. In this example, the proposed identification scheme is compared with a classical ANN identifier, and we present a statistical analysis of such comparison. It is shown in simulations that the identification error of the proposed homogeneous algorithm has faster convergence and less oscillations.