On recovering of unknown constant parameter by several test controls

We consider a control system involving a constant vector parameter, which is unknown to a controlling person; only a set of possible values of this unknown parameter is supposed to be known. We study the problem on approaching a targeted set at a prescribed time. To resolve the control problem at the beginning of the motion, we recover the unknown parameter by a successive short-time application of several test controlling vectors to the control system and observing then the reaction of the system. The choice of test vectors is proposed to make by minimizing the error of recovering of the unknown parameter. In contrast to previous works, we consider a more general case, when one test controlling vector is not enough for the unique recovering of the unknown parameter and moreover, for approximating the velocity of the motion, we employ a central difference derivative instead of the right difference one. As an example, we consider the problem on controlling a pendulum with unknown dissipation coefficient and elasticity coefficient of the spring.