Closed-loop Identification Problem Research Articles

An Open-loop Solution to the Approximate Closed-loop Identification Problem

Abstract The identification of a plant in the presence of feedback is troubled by the dependency of the controlled plant input and the noise disturbances. Analysis of the closed-loop identification problem by means of the algebraic theory of fractional representations has led to a framework for open-loop identification of the coprime factors of the unknown plant. As a consequence the framework allows the feedback controlled plant to be identified by the application of any existing open-loop identification method. This feature is illustrated by an example of nonparametric identification. Moreover unlike any other closed-loop identification scheme the presented framework offers a means for comprehensible and manageable parametric approximate transfer function estimation of the feedback controlled plant.

Optimal Adaptive Control of Linear-Quadratic-Gaussian Systems

We consider the problem of adaptively controlling an unknown linear-Gaussian system with a standard quadratic cost criterion, including a control cost. By means of a counterexample, it is shown that a commonly mentioned adapative control scheme can lead to severe problems. To overcome this, a new adaptive control law, based on biasing the usual least-squares parameter estimation criterion with a term favoring parameters associated with lower optimal costs, is introduced. A salient feature of this adaptive control scheme is its imperviousness to the closed-loop identification problem. Properties such as closed-loop system identification, convergence of the adaptive control law to an optimal control law, overall stability of the controlled system and optimality with respect to the long-term average cost of the adaptive controller are proved.

The Global Error Approach to the Convergence and Accuracy of Complex Recursive Identification Algorithms

The global error is the identification error expressed expiIcItly as a function of all unknown system parameters, model parameters and external system inputs. It is used to transform the difficult problem of mean-square convergence and accuracy testing for recursive identification algorithms into a relatively simple problem of determining the properties of the solution for a polynomial equation. The method is introduced for the simple problem of closed-loop identification of time-discrete systems. Its full power is demonstrated for the case of the self-tuning regulator and self-tuning predictor.