Projection Methods for Order Reduction of Optimal Human Operator Models

Human operator models developed using optimal control theory are typically complicated and over-parameterized, even for simple controlled elements. Methods for generating less complicated operator models that preserve the most important characteristics of the full order model are developed so that the essential features of the operator dynamics are easier to determine. A new formulation of the Optimal Control Model (OCM) of the human operator is developed that allows order reduction techniques to be applied in a meaningful way. This formulation preserves the critical neuromotor dynamics and time delay characteristics of the human operator. The Optimal Projection (OP) synthesis technique is applied to a modified version of the OCM. Using OP synthesis allows one to determine operator models that minimize the quadratic performance index of the OCM with a constraint on model order. This technique allows analysts to formulate operator models of fixed order. Operator model reduction methods based on variations of balanced realization techniques are also developed since they reduce the computational complexity associated with OP synthesis yet maintain a reasonable level of accuracy. Computer algorithms are developed that insure that the reduced order models have noise to signal ratios that are consistent with OCM theory. The OP method generates operator models of fixed order that are consistent with OCM theory in all respects, i.e. optimality, neuromotor lag, time delay, and noise to signal ratios are all preserved. The other model reduction techniques preserve these features with the exception of optimality. Each technique is applied to a variety of controlled elements to illustrate how performance and frequency response fidelity degrade when the order of the operator model is reduced.