Salp Swarm Optimization-Based Approximation of Fractional-Order Systems with Guaranteed Stability

In this paper, we introduce the salp swarm optimization algorithm (SSOA)-based novel model reduction algorithm for simplifying commensurate and incommensurate fractional-order systems. In the case of commensurate fractional-order systems (CFOSs), the presented method converts it into a non-fractional-order system first. Then, we implement the SSOA with the stability equations to find a non-fractional-order approximant. Finally, the non-fractional-order approximant is transformed to determine the proposed reduced-order CFOS. It is also demonstrated using numerical examples that some existing methods fail to achieve the stability claim. On the other hand, the stability of the proposed fractional-order approximants is ascertained by incorporating stability equations along with SSOA. Further, the proposed method is extended for the model reduction in incommensurate and unstable fractional-order systems. In this case, the Oustaloup approximation is used along with the SSOA and stability equations to obtain the proposed non-fractional-order approximation. The simulation results corroborate the performance of the suggested method in both cases and establish its transcendency. The obtained results showcase the efficacy of optimization in simplification of fractional-order systems. The work also highlights the importance of order reduction in practical engineering and scientific applications of fractional-order systems.