Implementation of Legendre Neural Network to Solve Time-Varying Singular Bilinear Systems

Bilinear singular systems can be used in the investigation of different types of engineering systems. In the past decade, considerable attention has been paid to analyzing and synthesizing singular bilinear systems. Their importance lies in their real world application such as economic, ecological, and socioeconomic processes. They are also applied in several biological processes, such as population dynamics of biological species, water balance, temperature regulation in the human body, carbon dioxide control in lungs, blood pressure, immune system, cardiac regulation, etc. Bilinear singular systems naturally represent different physical processes such as the fundamental law of mass action, the DC motor, the induction motor drives, the mechanical brake systems, aerial combat between two aircraft, the missile intercept problem, modeling and control of small furnaces and hydraulic rotary multi-motor systems. The current research work discusses the Legendre Neural Network’s implementation to evaluate time-varying singular bilinear systems for finding the exact solution. The results were obtained from two methods namely the RK-Butcher algorithm and the Runge Kutta Arithmetic Mean (RKAM) method. Compared with the results attained from Legendre Neural Network Method for time-varying singular bilinear systems, the output proved to be accurate. As such, this research article established that the proposed Legendre Neural Network could be easily implemented in MATLAB. One can obtain the solution for any length of time from this method in time-varying singular bilinear systems.