Parameter estimation for nonlinear dynamic systems from a feedback control viewpoint

The estimation of time-variant parameters in nonlinear models remains as an open problem. In this work, we propose a new approach to addressing this problem by tuning weighting factors in the least-squares dynamic optimization. Through analysis of the solution procedure of the resulting optimization problem, it is found that parameter estimation with a weighted least-squares method is equivalent to a multi-variable closed-loop control system. The weighting factors in the objective function are equivalent to the controller parameters. Like any control system synthesis, the tuning can be made based on the output-input sensitivity analysis. The effectiveness of the approach is illustrated by estimating tray efficiencies and feed composition of a heat-integrated distillation column system.