Parametric Optimizationof a Nonlinear Model in Tumor Cell Growth Identification

Abstract. This paper presents an identification method for time-varying objects that involves mathematical models with parametric tuning. The deviation of object’s transients and its mathematical model are estimated in terms of a quadratic performance criterion; the parametric tuning of the object model is a constrained optimization problem. The parametric optimization algorithm is developed using the vector projection property in a Krein space and the second Lyapunov method for a targeted change in the model parameters. The method is applied to estimate parameters in a tumor cell growth model. The nonlinear model describes the relationship between the populations of normal, immune, and tumor cells that can be measured in the presence of Gaussian white noise. Numerical simulation illustrates the design procedure and shows the effectiveness of this method.

Keywords: parametric optimization, identification, cost function, nonlinear differential equations, Lyapunov method, Wiener–Hopf equation.