Proceedings of International Conference on Applied Innovation in IT
2025/12/22, Volume 13, Issue 5, pp.575-581

Mathematical Foundations for Modeling and Scaling of Dynamic Systems


Olga Filina, Olimjon Toirov, Azat Khusnutdinov, Valerei Butakov, Olga Salnikova and Elena Kugergina


Abstract: The increasing complexity of electric vehicle (EV) powertrains – integrating multi-domain interactions among traction motors, battery packs, and power electronics – demands mathematically rigorous yet computationally efficient modeling frameworks. This paper presents a structured review of the mathematical foundations for modeling and scaling of dynamic systems, with emphasis on EV applications. Three core analytical tools are examined in depth: 1) state-space representation as a unified multi-domain modeling formalism; 2) similarity transformations for complexity reduction while preserving essential system invariants such as eigenvalues, characteristic polynomials, and transfer functions; and 3) scaling techniques, including dimensionless parameterization and transfer function normalization, for cross-platform simulation efficiency. A structured mapping links these methods to specific EV subsystems: traction motors (4th–8th order systems), battery packs (2nd–10th order equivalent circuits), and power inverters (3rd–6th order systems), identifying the most appropriate scaling strategy for each. The reviewed framework supports scalable simulation, model-based diagnostics, and control system design, bridging high-fidelity physics-based models and computationally efficient representations required for real-time embedded applications. This paper serves as a foundational methodological resource for researchers and practitioners in EV engineering and control systems.

Keywords: Dynamic Systems, State-Space Models, Similarity Transformations, Scaling Methods, Electric Vehicles, Model Reduction, Control-Oriented Modeling.

DOI: Under indexing

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