A stable and efficient hybrid polynomial-diagonal recurrent neural network controller for mobile robot applications

This paper introduces a novel hybrid polynomial-diagonal recurrent neural network controller (HP-DRNNC) for controlling the wheel speeds of a mobile robot. The proposed NN structure contains hidden neurons with self-feedback, i.e., diagonal recurrent. Thus, the proposed HP-DRNNC merges the merits of the polynomial activation function and the memory capability of the diagonal recurrent neurons. Moreover, the primary objective of this work is to reduce computational complexity by employing a minimal number of weights, only six adjustable weights are utilized in the proposed architecture. Additionally, this work ensures the stabilization of the learning algorithm and optimizes the convergence speed of the learnable parameters through the application of Lyapunov stability theory. Furthermore, an adaptive learning rate rule is derived to guarantee the optimal learning performance for the proposed HP-DRNNC. The main novelty of this work lies in the proposed HP-DRNNC structure, which combines low computational complexity with robust adaptive control. Unlike conventional adaptive neural controllers, the proposed controller requires significantly fewer tunable parameters and shorter computation time while preserving accurate online learning and Lyapunov-based stability. Consequently, it enables efficient sample-by-sample adaptation without relying on a pre-collected dataset, making it well suited for real-time control applications. In this study, the proposed HP-DRNNC is implemented for the control of a mobile robot capable of executing multiple missions. Experimental results demonstrate the robust and superior performance of the proposed HP-DRNNC compared to other existing controllers across all practical missions. The proposed HP-DRNNC improved the performance indices over other controllers by 51% and 40% in some tasks, such as mass uncertainty and external disturbance, respectively.