Parameter estimation using multiparametric programming for implicit Euler’s method based discretization

Abstract

This work presents a study that aims to compare two discretization methods for solving parameter estimation using multiparametric programming. In our earlier work, parameter estimation using multiparametric programming was presented where model parameters were obtained as an explicit function of measurements. In this method, the nonlinear ordinary equations (ODEs) model was discretized by using explicit Euler’s method to obtain algebraic equations. Then, a square system of parametric nonlinear algebraic equations was obtained by formulating optimality condition. These equations were then solved symbolically to obtain model parameters as an explicit function of measurements. Thus, the online computation burden of solving optimization problems for parameter estimation is replaced by simple function evaluations. In this work, we use implicit Euler’s method for discretization of nonlinear ODEs model and compare with the explicit Euler’s method for parameter estimation using multiparametric programming. Complexity of explicit parametric functions, accuracy of parameter estimates and effect of step size are discussed.