Stable On-the-Fly Learning for Dynamic Neural Networks with Delayed Inputs

This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov¿Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization¿projection¿devectorization implementation suitable for online use. Compared with delay-dependent functionals, the proposed approach avoids state augmentation and reduces computational overhead while preserving formal guarantees. The analysis is developed for a fixed delay, while extensions to bounded time-varying and multiple delays are discussed. Numerical studies of geodesic motion, an aircraft model, and a head-rotation task demonstrate fast transients, accurate prediction, and graceful degradation as the delay increases. The results indicate that stable learning with delayed inputs is practical and competitive with recent delay-aware identifiers in terms of accuracy, complexity, and reproducibility. © 2013 IEEE.

Stable On-the-Fly Learning for Dynamic Neural Networks with Delayed Inputs Academic Article in Scopus