Approximating nonlinear dynamics with linear models remains a fundamental challenge in control theory and computational sciences. This talk introduces a dynamic matching framework that bridges the gap between complex nonlinear behaviours and the efficiency of linear analysis. Unlike traditional static linearization, which often fails as the system deviates from a fixed operating point, the proposed framework employs a recursive, iterative linearization strategy. The core mechanism involves a robust system identification phase to determine local model parameters, followed by an adaptive modelling phase that updates the system solution within an iterative loop. By dynamically recalculating linear coefficients to match the current state of the nonlinear manifold, the framework ensures local validity across the entire trajectory. For illustration, we apply the framework to study the Van der Pol oscillator, the prey-predator model and the continuous stirred-tank reactor model. Simulation results demonstrate that this framework achieves high-accuracy convergence while significantly outperforming direct nonlinear solvers in computational speed. By leveraging high-performance optimization, our approach replaces costly, complex nonlinear function evaluations, enabling the scalable application of proven linear control methods to real-world engineering problems.

Keywords:

Nonlinear Dynamics, Iterative Linearization, System Identification, Adaptive Modelling, Computational Efficiency

Sie Long Kek, PhD, CQRM, is currently a senior lecturer in the Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia (Pagoh Campus). He received his M.Sc. and Ph.D. in mathematics from Universiti Teknologi Malaysia, Johor, Malaysia, in 2002 and 2011, respectively. He was a research associate at Curtin University of Technology in 2009 during his Ph.D. study. His research interests include optimization and control, operational research and management science, modelling and simulation, parameter estimation, Kalman filtering, and computational mathematics. He has published over 60 papers in refereed journals and six (6) book chapters. He reviews peer-reviewed research journals, including Automatica, Optimal Control, Applications and Methods, International Journal of Control, Heliyon, Journal of Industrial and Management Optimization, Measurement and Control, Hindawi Journal of Mathematics, and MDPI Journal of Risk and Financial Management. He has hosted three (3) research projects supported by the Ministry of Education Malaysia. He has supervised five (5) master's and three (3) Ph.D. students. Since 2015, he has been a certified quantitative risk management (CQRM) fellow. From 2021 to 2023, he was appointed head of the research focus group, Numerical Simulation and Applications (NSA).