Optimal Feedback Controls for Parameter Identification.

摘要

This dissertation investigates improving the estimates of unknown constant parameters in the plant and control matrices of a linear discrete system from noisy measurements by the use of a control consisting of a feedback term and open-loop term. The feedback term allows one to move the poles of the system to location which improve the information in the output about the parameters beyond that attainable with only open-loop control inputs. An energy constraint is placed on the open-loop term of the control and the closed-loop poles are required to remain within a predetermined constraint space. Output feedback is used and for the cases where the dimension of the output is less than the dimension of the system states, an additional consistency constraint on the closed-loop poles is required. The criterion that has been used is the maximization of the trace or weighted trace of the Fisher information matrix. A graident projection algorithm has been developed that maximizes this scalar function while maintaining the poles within the constraint space. This procedure results in maximizing the sum of a maximum eigenvalue of a positive semi-definite matrix and a term resulting from the feedback of measurement noise into the process equations. The variable in this maximizaton procedure is the feedback matrix. The optimal open-loop control sequence is a scaled eigenvector corresponding to the maximum eigenvalue. The procedure is developed for the multiple parameter and multiple input control cases. Examples are used to demonstrate the enhancement of parameter identification gained by adding feedback control to an open-loop control input. (Author)