Design for minimum probabilistic error of continuous linear control systems subject to constraints

A NEWLY DEVELOPED approach to the synthesis of control systems has been based on “probabilistic” or “end-sigma” error.1 These names denote the concept of an average p“enalized error for such times when the output of the control system is actually used. Detail design processes for continuous2 or sampled-data3 linear systems have been developed to yield linear systems operating with minimum probabilistic square errors. This paper shows that constraints, specifically an acceleration constraint on the output, can be included in the design process for minimum probabilistic square error. Only continuous systems are treated in this paper, but extension to sampled systems is straightforward.