Delay-Adaptive Finite-Dimensional Control of Systems with Unknown Short Input Delay

Delay-adaptive predictor-feedback controllers are effective for handling unknown input delays of arbitrary length. However, when the delay is much shorter than the system's time scales, the predictor's infinite-dimensional part becomes negligible, and a simpler finite-dimensional controller may offer a more practical solution. In this note, we extend the applicability of such finite-dimensional controller by relaxing the conventional short-delay assumption, allowing the delay to approach the system's dominant time constant. Specifically, we propose an adaptive control framework that combines a delay identification algorithm with a state-feedback controller, enabling delay-adaptive pole placement and achieving near-optimal system performance without explicit delay compensation. Case studies, including a solar tracking application, demonstrate that the proposed method can outperform both full and truncated delay-adaptive predictor-based controllers.