Persistently-exciting signal generation for Optimal Parameter Estimation of constrained nonlinear dynamical systems

Abstract

This work presents a novel methodology for Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation of constrained nonlinear systems. It is proposed that the evaluation of each signal must also account for the difference between real and estimated system parameters. However, this metric is not directly obtained once the real parameter values are not known. The alternative presented here is to adopt the hypothesis that, if a system can be approximated by a white box model, this model can be used as a benchmark to indicate the impact of a signal over the parametric estimation. In this way, the proposed method uses a dual layer optimization methodology: (i) Inner Level; For a given excitation signal a nonlinear optimization method searches for the optimal set of parameters that minimizes the error between the outputs of the optimized and benchmark models. (ii) At the outer level, a metaheuristic optimization method is responsible for constructing the best excitation signal, considering the fitness coming from the inner level, the quadratic difference between its parameters and the cost related to the time and space required to execute the experiment.

Keywords: Constrained systems parameter estimation; Non-linear systems; Optimal Input Design; Optimal Parameter Estimation; Optimal signal generation; Optimization in parameter estimation.