Neural network-based simplified optimised backstepping control for attitude tracking of a 2-DOF helicopter system

This article proposes an adaptive optimised control strategy for attitude tracking in a 2-degrees-of-freedom (2-DOF) helicopter system by applying optimised backstepping (OB) technique. In order to derive the optimised control, the neural network (NN) approximation is implemented to obtain the estimated solution of Hamilton–Jacobi–Bellman (HJB) equation, and the NN is trained to utilise a simplified Reinforcement learning (RL) algorithm in the identifier–critic–actor architecture, which obtaining the training laws from the negative gradient of a straightforward positive function, rather than utilising established optimal control methodologies. The system's closed-loop error signals are proven to be Semi-Global Uniformly Ultimately Bounded (SGUUB), and output follows the reference signal precisely, as verified through Lyapunov analysis. Comparative simulation results demonstrate the effectiveness of the proposed strategy in practical engineering fields, particularly in optimising control for real-world systems.