A Novel Reduction Approach for Linear System Approximation

In this study, a novel system reduction approach is suggested for a linear time-continuous system. Motivated by various optimization techniques and reduction problems in system engineering, a new search algorithm, namely ant lion optimization (ALO), is being utilized for system approximation. This algorithm is based on the random walk of an ant lion for searching the food. Firstly, the approximated system is formulated by reducing the integral square error (ISE) between the higher-order and proposed approximated system using ALO. To validate the high efficiency and accuracy of the suggested approach, it is tested on four benchmark systems maximum up to 84th order including a time-delay system. It is revealed that approximated system characteristics, achieved by the suggested approach, are much closer to the characteristics of the higher system. Further, it is also revealed that the transient, steady-state, and frequency response characteristics of the higher-order system are preserved by the suggested approximated system. Additionally, the lowest value of ISE is observed with the proposed approximated system as compared to other approximated systems already available. Furthermore, the efficacy of the suggested approach is also investigated in terms of final convergence rate and CPU usage time by employing well-known the genetic algorithm (GA) and particle swarm optimization (PSO) to obtain approximated systems.