The Global Error Approach to the Convergence of Closed Loop Identification, Self Tuning Regulators, and of Self Tuning Predictors

摘要

The global error is the identification error expressed as a function of unknown system parameters, model parameters, and external system inputs. It provides a convenient tool to test mean-square convergence for a number of complicated estimation problems. It is shown, how the global error approach can be used to give a simple explanation of well-known closed loop system models is shown. A self tuning regulation is analyzed for the general case of a difference equation model. A stationary time series to be predicted N-steps ahead is described and a unique solution for the predictor parameters is found which correspond to the optimum prediction parameters.