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An abstract simulator design problem is formulated as follows: we are given a dynamic system Sa called the actual system and another dynamic system SS called a simulator for Sa. Furthermore, we are given an input signal which drives the actual system Sa. The problem is to find an operator, properly constrained, which generates the input to the simulator Ss on the basis of the input to Sa so that the discrepancy between the output of Sa and Ss is as small as possible. This abstract simulator design problem is brought to the form of an optimal control problem and then solved for the linear-quadratic-Gaussian special case. Next the soluiion of the abstract simulator problem is applied to the design of motion generators for flight simulators. A fairly elaborate mathematical model of the vestibular organs is used. The optimization criterion that is selected is the mean-square difference between the physiological outputs of the vestibular organs for the pilot in the airplane and for the pilot in the simulator. The dynamical equations are linearized, and the input signal is modeled as a random process with a rational power spectral density. Subject to the above assumptions, the optimal structure of the motion generator for the simulator, also called a "washout filter," is derived. This method stands in contrast to existing design schemes for motion generators which generally assume a certain fixed structure for the motion generator and concentrate on optimizing its parameters.