Analysis of motion separation by control for two identical pendulums

The paper studies the possibility of separating the motions of two identical dynamic systems using a single scalar action generated by a feedback mechanism. Such a problem may arise with underactuated control of oscillatory mechanical systems, with selective control of individual molecule systems, etc. A typical case is studied when separation must be performed based on the energy level of subsystems. To solve the problem, it is proposed to synthesize feedback control. The control algorithm is based on the speed gradient method extended to account for constraints. To design control under constraints the inner penalty function is used. Its operability in this case follows from the invariance of the subsystem energies in the absence of control. It is shown that even a small difference in the initial states of the controlled systems allows the required separation to be achieved, and the result depends weakly on significant changes in the parameters of the controlled system and on the presence of disturbances. Finally, the result depends weakly on the parameters of the controller (gain gamma) and the strength of the penalty alpha.