Model reduction for dynamical systems with MIMO extension and an enhanced cuckoo search algorithm

• Published in: International journal of dynamics and control Vol. 13; no. 9
• Main Authors: Ben Slimane, Kamel, Tmar, Zied, Besbes, Mongi
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.09.2025
• Subjects: Complex systems; Complexity; Computing costs; Convergence; Dynamical systems; Heuristic methods; Model reduction; Parameter sensitivity; Search algorithms; Sensitivity analysis; State space models
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-025-01804-5

This paper explores advanced techniques for reducing the order of high-order systems, with a focus on methods inspired by metaheuristic optimization. It begins with an overview of traditional approaches, such as balanced truncation using state-space representation and Cholesky transformation. These classical methods are discussed in terms of their advantages and limitations, particularly regarding computational complexity, the accuracy of the reduced model, and the uncertainty related to the selection and computation of reduction parameters. An extension to MIMO systems is proposed and applied to a methanization process. The study then introduces an enhanced variant of the Cuckoo Search Algorithm (CSA), incorporating Lévy Flight, aiming to improve convergence and solution quality. To assess the performance of the proposed method, a new section provides a systematic quantitative comparison of reduction techniques, including a summary and discussion, benchmarking against standard metaheuristic algorithms, frequency-domain validation, scalability to complex systems, preservation of transient behavior, computational cost, convergence and sensitivity analysis, stability in MIMO model reduction, and empirical parameter selection. The results highlight the robustness, efficiency, and general applicability of the enhanced CSA in the context of model order reduction.