Parameter Identification in Nonlinear Systems Using PD Controllers as Penalty Functions

Abstract

The identification of parameters in nonlinear systems using a partial set of experimental measurements is considered in this paper. The estimation of these parameters introduces an optimization problem. For parameter estimation, the use of gradient-based optimizers often converges to a local minimum rather than the global optimum. To overcome the local convergence of the parameters, a PD controller algorithm is implemented for estimation. The addition of a morphing parameter with a proportional-derivative controller (PD) to the system equation transforms the objective function into convex, and the optimization is performed using a gradient-based optimizer. To illustrate the nonlinear parameter estimation using the present approach, a numerical example of Van der Pol-Duffing oscillator is presented. A comparative analysis is then carried out with global optimization methods, such as genetic algorithm (GA) and particle swarm optimization (PSO) techniques. The numerical results confirm that the PD controller algorithm is superior in terms of computational effort and convergence efficiency.