This talk discusses applying a linear optimal control model to predict the solution curve of nonlinear dynamical systems. Since general dynamical systems are nonlinear and complex, obtaining their solution curves is often challenging. Here, we assume the solution curve of a nonlinear dynamical system exists. We begin to propose a linear state equation with a control input. The aim is to find an admissible control law for minimizing a quadratic performance index. We identify the optimal state trajectory after designing the optimal control law. Then, we introduce a tracking problem. The aim is to minimize the output differences between the nonlinear system and the model. By using the gradient descent method, the tracking problem is solved, in turn, to estimate the model parameters. The model solution closely tracks the nonlinear system's solution curve upon convergence. For illustration, we study two examples, one for a nonlinear system and another for a historical dataset. The simulation results show the accuracy of the prediction solution with a small mean squared error value, and the computational algorithm demonstrates its high efficiency during the calculation procedure. These findings underscore the use of a linear optimal control model for handling dynamic system prediction and providing a satisfactory outcome, encouraging us to explore the linear optimal control model further for dynamic predictive modelling.

Keywords: 

Dynamic System Prediction, Linear Optimal Control, Gradient Descent Method, Mean Square Error, Computational Algorithm 

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 the 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 50 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 two (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 is 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).   

Email: slkek@uthm.edu.my 

UTHM Staf Profile: https://community.uthm.edu.my/slkek 

SCOPUS ID: 35776335100

ORCID ID: 0000-0003-0425-4422

Publons ID: H-6498-2011

Google Scholar: https://scholar.google.com.my/citations?user=wWntPq4AAAAJ&hl=en