The problem for optimal restoration of the state of the system described by an integro-differential equation in the presence of errors in measurements

The problem of developing an optimal operation is investigated for restoration of the state of the system described by an integro‐differential equation in the presence of errors in measurements. By the method of separation of variables the solution of the problem is brought to the solution of the problem of observation with a real signal of the infinite system of ordinary differential equations. For each harmonic, amplifying a signal coming from the system, a universal optimal operation is developed, which provides a way of restoring the deviation from the equilibrium position and the speed of all points of the system.