Discrete-Time System Approximation Using Hybrid Method Based on Fuzzy C-Means Clustering

A mathematical technique named the discrete-time system approximation is used for approximating higher-dimensional system to their lower-dimensional system by retaining the essential characteristics. Hence, a new hybrid technique is presented in this paper for discrete-time system approximation. The technique presented in this paper is developed by combining fuzzy C-means clustering (FCMC) and cuckoo search optimization (CSO) technique. Firstly, to get steady lower-dimensional system, the denominator polynomial is derived by FCMC technique. Secondly, the CSO technique is being employed to formulate numerator polynomial of the lower-dimensional/approximated system. The proposed hybrid method is tested on higher-dimensional test systems considered from the literature to derive lower-dimensional systems. Further, the efficiency of the suggested hybrid technique is justified on comparison of time domain characteristics and various performance indices. The time responses of higher- and lower-dimensional systems are plotted with respect to unit step input. It is observed that lower-dimensional system’s response derived from suggested hybrid method is found to be closed to the considered test system’s response. Furthermore, it reveals that the suggested hybrid technique gives the minimum performance indices values and hence has a better overall performance. One of the applications of the proposed hybrid method may be explored in the discrete-time interval system approximation.