Accession Number : AD0835644

Title :   OPTIMAL CONTROL FOR INFORMATION MAXIMIZATION IN LEAST-SQUARE PARAMETER ESTIMATION,

Corporate Author : UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Nahi, Nasser E. ; Wallis, David E., Jr

Report Date : JAN 1968

Pagination or Media Count : 100

Abstract : System identification (the process of obtaining a mathematical model to characterize the dynamics of a system from input-output observations) is often accomplished by estimating the constant parameters of an otherwise known model. In most systems, the 'quality' of the estimates (for example, the variance of the estimates) depends on the input as well as on the form of the estimator. It is logical to attempt to choose the input to reduce, say, the variance of the estimators. The problem of determining the optimal input is made difficult by constraints on the admissible inputs and by the fact that the form of an optimal estimator (having, say, minimum variance) for processing the system output is often unknown. A useful relationship for determining the 'best' input is the Cramer-Rao lower bound (the 'information limit') on the variance of the estimators. An important result is that the formulation of this lower bound depends only on the input and the form of the system, and not on the estimator to be used. Effectively, the lower bound gives the (minimum) variance which would be obtained by using an optimal (efficient) estimator. Practical procedures are developed to select system inputs to minimize the lower bound, irrespective of the form of the estimator. Thus, the system output automatically becomes such as to permit minimum-variance estimation of parameters, while avoiding consideration of the complicated form of actual estimators to be used. (Author)

Descriptors :   (*OPERATIONS RESEARCH, CONTROL SYSTEMS), (*INFORMATION THEORY, CONTROL SYSTEMS), OPTIMIZATION, SENSITIVITY, MATHEMATICAL PREDICTION, MATHEMATICAL MODELS, LEAST SQUARES METHOD.

Subject Categories : Operations Research
      Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE