Effect of uncertainties on the control performance of linear systems with unknown parameters and trajectory confidence tubes

This investigation deals with the quantitative assessment of the effects of two sources of uncertainty on the quadratic performance index used for controlling linear econometric models. The uncertainties that are most important are the errors in the parameters´ estimates and the additive noise entering the dynamic equations. Errors in measurements are not considered here. An algorithm based upon the open-loop feedback concept is presented that evaluates the increase in the cost due to parameter errors. The parameters are modelled as random variables with known statistics up to second order, assumed not to change during the control period. This is equivalent to assuming that during the control period the quality of the parameters´ estimates will remain essentially the same. These results can be used to assess the potential usefulness of adaptive control for a problem.