Neural network-based state observation utilizing a history-of-error performance index

Accurate state estimation is crucial for the control and monitoring of multivariable nonlinear systems. Neural network-based observers offer promising solutions due to their universal approximation capabilities; however, maintaining precision and robustness in the presence of nonlinearities and parametric uncertainties remains a significant challenge. This paper presents an adaptive neural network observer that incorporates a history-of-error term into the weight update rules of a modified backpropagation algorithm. An e-modification term is introduced to ensure bounded state-estimation errors, with stability formally established through a Lyapunov-based analysis. Simulation and experimental studies on a one-link arm under gravity, actuated by a DC motor, demonstrate that the proposed observer can significantly enhance the estimation accuracy and convergence speed when compared to conventional neural network observers. Comparative studies indicate an approximate 50% improvement in state estimation and control accuracy, highlighting the effectiveness of the proposed approach.