Neural network‐based non‐linear adaptive controller design for a class of bilinear system

This study presents a novel neural network (NN)‐based non‐linear adaptive control strategy for the global stability of multi‐input–multi‐output state‐control homogeneous bilinear system (BLS) at the equilibrium position. Although this class of non‐linear system is neither piecewise nor feedback linearisable, conditionally stabilisable control system design can be utilised to generate multiple state transitions and corresponding control gains. The collected data was used to train a NN to obtain an optimal gain estimator. Then the optimal gain estimator was integrated into real‐time control system operation to adaptively compute control gains, ensuring that the controller is continuously adjustable to changing behaviour of the system. The proposed design was shown, through an illustrative example, to overcome the stability limitations of traditional controllers for the investigated class of BLS. Furthermore, discussions about the utility of the traditional control and learning system integration, as well as stability analysis of the proposed scheme were presented.