In the article a problem of mathematical models construction for oscillatory mechanical systems (OMS) with complex (chaotic) dynamics is considered. The mathematical model of system is constructed with application of the aggregative method. The device for OMS control with use of the computer is described. Verification of the obtained model on the basis of laboratory experiments results is made. Pulse-number algorithm of OMS control is proposed and checked with use of laboratory set-up. State estimation recursive algorithm is proposed.