Reliability-Gated Residual Prediction for Bounded Nonlinear Responses Under Matched Excitations

Abstract Abstract-The control value of a residual predictor depends onits effect on the closed-loop response neighborhood. For known-input-gain, second-order, discrete-time nonlinear systems withmatched uncertainties, this paper develops a reliability-gatedadaptive controller that admits causal Fourier residual predic-tions when their one-step errors are admissible for feedback.Rejection removes direct compensation and strengthens robustfallback adaptation. A common composite Lyapunov analysis es-tablishes practical uniformly ultimately bounded dynamics underadmissible switching without dwell time, and gives conditionaldescent-radius comparisons. A worst-case-window trigger sup-plies a sufficient admissibility condition under a prediction-errorvariation bound. Simulations with slowly modulated, broadbandand temporary predictability-loss excitations characterize accep-tance, tracking and control-effort tradeoffs against non-predictiverobust, observer, neural and always-on baselines. A separatebounded companion instantiates conservative numerical certifi-cates. The results support conditional use of residual structurein feedback, without uniform performance dominance.