Integral estimates of moments and the synthesis of nonlinear regulators

A new solution of the problem of the analytic design of stable linear stationary object regulators with modulusconstrained control actions, a fixed value of the sum of integrals of the moduli of the coordinate linear forms under stochastic or determined initial conditions is suggested. The optimal relay-operated controls and the analytic expressions for all the coefficients of these controls are given. The same sums as in linear controls obtained in the previous article 1 serve as arguments of optimal relayoperated controls. The optimal coefficients are simply expressed by the integral quadratic estimations of the object weighting functions which makes possible an experimental determination and self-adjustment of optimal controls. With optimal relay-operated controls the object acquires a nonperturbation property with regard to the limited forces.