An orthogonal data-driven Neural Network observer for simultaneous state and unknown input estimation for Linear systems

This paper presents a novel approach for state and unknown input (UI) observer in single-input single-output (SISO) linear time-invariant (LTI) systems. An Orthogonal Neural Network (ONN), which does not require traditional training or offline learning, is incorporated to approximate the unknown input. The proposed method extends the system state to include the ONN weights, creating a new LTI system. Leveraging the structure of orthogonal activation functions, a suitable algorithm for the extended state dynamics is derived. The observer gain is computed using Linear Matrix Inequalities (LMI), ensuring stability and attenuating the approximation error. Unlike existing methods, this approach requires no assumptions about the unknown input, such as matching conditions or boundedness. A numerical example demonstrates the effectiveness of the proposed scheme.