ESTIMATION OF NONLINEAR SYSTEM STATES AND PARAMETERS BY REGRESSION METHODS.
Interim technical documentary rept.,
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES ENGINEERING CENTER
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Modern theories of optimal control are generally based on an assumption that a precise quantitative mathematical model exists for a dynamic system which is to be controlled or observed. In fact, such models are often lacking and must be inferred from experimental response data. When basic physical theory is sufficient to permit the object involved to be described by a differential equation with certain free parameters, the determination of a quantitative model becomes a problem in statistical estimation. This report formulates nonlinear dynamic system state and parameter estimation as a regression problem. An attempt is made to treat least squares regression, maximum likelihood estimation, and Bayes estimation from a unifying point of view. Experimental results relating to the nonlinear pendulum equation and to the ballistic vehicle atmospheric re-entry equation are included. These results show that it is possible to construct general algorithms for the automatic determination of parameter vectors by a digital computer. Author