Pseudo predictor for tracking control of fully actuated nonlinear systems with a constant input delay and application to a two-stage chemical reactor

The tracking control of nonlinear systems with input delays presents a significant challenge, particularly when traditional predictors suffer from numerical instability due to unstable open-loop dynamics. To address this issue, this paper investigates the tracking control problem for fully actuated nonlinear systems with a constant input delay by synergizing the fully actuated system (FAS) approach with a pseudo predictor strategy. This strategy predicts future tracking errors by integrating an FAS-derived linear stable error dynamics, thus avoiding the instability arising from the prediction based on the potentially unstable open-loop system. Furthermore, a two-layer stability analysis framework is established. The outer-layer tracking error system is input-to-state stable with respect to the inner-layer prediction bias. Based on this property, the prediction bias dynamics can be separated from the tracking error dynamics, and the asymptotic stability of the tracking error follows from the prediction bias being stabilized by Lyapunov-Krasovskii theory. The effectiveness of the proposed method is verified on a two-stage chemical reactor, demonstrating that the proposed pseudo predictor outperforms an open-loop predictor in both computational efficiency and robustness against process noises.