A fast robust output tracking approach based on the GRU-ARX model with application to quadrotor

This paper concentrates on addressing the heavy computational burden caused by computation-intensive operations in online robust output tracking control processes for multi-input multi-output nonlinear systems. To improve the online computational efficiency of deep learning model-based controllers for compatibility with the sampling frequency requirements of fast-responding nonlinear systems, a novel robust control framework that combines offline-trained gated recurrent unit-based auto regressive exogenous model with adaptive triggering strategy is developed. Firstly, the proposed approach utilizes the hybrid deep learning model to capture the nonlinear dynamics for advanced system identification. Secondly, a dual-mode adaptive robust control strategy is formulated based on the pseudo-linear structure of this model to dynamically manage the controller updating behavior. This strategy consists of two aspects: the offline calculations for co-designing the triggered matrices and control laws through the linear matrix inequality-based synthesis with asymptotic invariant ellipsoids, and an online update mechanism that evaluates the triggering condition to determine whether to execute a search operation for the optimal solution within the offline precomputed list. Additionally, the closed-loop stability properties of the system under the proposed framework is established theoretically. Finally, the proposed algorithms are successfully conducted on a real quadrotor platform. Comparative real-time control experiments involving step tracking and anti-interference demonstrate that the adaptive triggering robust controllers can effectively alleviate the online computational burden without sacrificing the control performance roughly. These results indicate that the online computational efficiency is improved by about 79 % in step tracking and 85 % in anti-interference experiments. This framework proves particularly effective for fast-dynamic systems, facilitating the real-time implementation of deep learning model-based robust control methods.