Adaptive Iterative Learning Control for Uncertain MIMO Systems with Application on Underwater Robot Trajectory Tracking

This paper addresses the trajectory tracking control problem of underwater robots operating in uncertain underwater environments. An adaptive iterative learning control algorithm is proposed to handle external disturbances caused by environmental uncertainties, as well as system challenges including non-uniform trial lengths and unknown control gain matrices. To improve trajectory tracking accuracy, an external disturbance compensation term is introduced, and the controller parameters are updated online using the tracking error between the desired and actual trajectories. Furthermore, an adaptive learning rate strategy is developed to compensate in real time for errors induced by external disturbances and other uncertainties, enabling dynamic optimization of the controller parameters based on the actual system trajectory. The proposed method relaxes the stringent traditional assumptions that require the control gain matrix to be known and strictly a symmetric positive definite (or negative definite). Based on Lyapunov stability theory and finite-time control techniques, a composite energy function is constructed to rigorously prove the convergence of the closed-loop system. Simulation results demonstrate that the proposed algorithm ensures satisfactory trajectory tracking accuracy and robustness for the underwater robot in the presence of external disturbances and various uncertainties, effectively solving the stabilization control problem in uncertain underwater environments.