Optimal Stabilization of Planar Motion of a Variable Mass Material Point under Integrally Small Perturbations

The present work considers the optimal stabilization problem in planar motion of a variable mass material point when integrally small perturbations act during a finite interval of time. The optimal stabilization problem of considered motion is assumed and solved. In direction of the polar coordinates introduced input controls, fully controllability of linear approximation of the obtained control system is checked up and the optimal stabilization problem of this system on classical sense is solved. Then, the problem will be limited to one input control, it is shown that the considered system is not fully controllable and for this case the optimal stabilization problem under integrally small perturbations of mentioned system is solved. For both cases optimal Lyapunov function is constructed, the optimal controls and the optimal value of performance index are obtained. A comparison between the optimal values of performance indexes proves that energy consumption at stabilization under integrally small perturbations is less than stabilization in classical sense.

کلیدواژه ها:

Dynamical Systems ، Optimal Control ، Optimal Stabilization ، Perturbation