A system in accordance with the invention uses an adaptive element to augment a filter for tracking an observed system. The adaptive element only requires a single neural network and does not require an error observer. The adaptive element provides robustness to parameter uncertainty and unmodeled dynamics present in the observed system for improved tracking performance over the filter alone. The adaptive element can be implemented with a linearly parameterized neural network, whose weights are adapted online using error residuals generated from the Filter. Boundedness of the signals generated by the system can be proven using Lyapunov's direct method and a backstepping argument. A related apparatus and method are also disclosed.