abstract
- Non-parametric identifiers are dynamic systems that produce approximate models based on input¿output paired data. This work develops a non-parametric identification algorithm for continuous systems based on the linear combination of functions that form a closed subset of a basis in a functional space. The algorithm considers the design of a differential form for the parameter adjustment, which is obtained using the second stability method of Lyapunov. Inspired by the gradient descent method, the proposed algorithm formally adjusts parameters despite the nonlinear relationships between parameters that define the identifier structure. Formal stability studies prove the explicit construction of parameter adjustment laws, highlighting the design conditions. This study shows the explicit design of an identifier with one single layer of activation functions in the basis, a single nested layer of such functions (like in a two-layer neural network), and a general form based on N-nested arrangements of functions like deep learning structures. This algorithm's approximation capacity is confirmed by comparing it with some methods based on Autoregressive and Hammerstein-Wiener Models, available in MATLAB®software. The comparison of the proposed approach gets at least similar results to the best obtained with the comparative strategies. The proposed technique introduces a general form of deep learning tools to identify the evolution of dynamic systems with uncertain mathematical models. © 2025 Elsevier B.V.