Curve tracking of nonlinear dynamic system using linear state-space model

In this paper, curve tracking of nonlinear dynamic systems is discussed. In mathematical modelling, a curve is defined as the solution of a dynamic system. Assuming the actual model of a dynamic system is unknown, we only have the solution curve of a system. Hence, tracking the curve becomes prominent in studying a nonlinear dynamic system. For this purpose, we propose a linear state-space model to track the curve of a nonlinear dynamic system. First, a least squares optimization problem is introduced, where the differences between the system and the linear model are defined. An adaptive parameter is introduced in the linear model, aiming to capture these differences. Second, the first-order necessary condition is derived, and the adaptive parameter is determined to update the curve of the linear model. Once convergence is achieved, the optimal solution curve of the linear model approximates the correct solution curve of the nonlinear system despite model-reality differences. Third, an example of a chemical kinetics system is studied for illustration. The simulation results show the efficiency of the computation algorithm, and the iterative solution demonstrates the accuracy of curve tracking. Therefore, using the linear state-space model to track the curve of the nonlinear dynamic system is satisfactorily handled.

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