Abstract
This paper discusses the synthesis of an optimal actuator of a multi-input oscillatory system, which is desirable from the viewpoint of a minimum energy control problem whose terminal time is not necessarily assumed to be very large.
That is, considering the situation such that a numerical approach has been adopted until now to the synthesis because of the high nonlinearity of a performance index, the paper derives a lower bound or an upper one for the optimal performance value in order that the optimality of the actuator can be checked in the execution of the numerical method. Three criteria named here as the determinant criterion, trace one, and min-max one are respectively used.
Furthermore, the paper shows that optimal actuator can be analytically solved even for the relatively small terminal time in the case where the terminal time satisfies a condition concerning the system natural angular frequencies and the degree of freedom of multiinput actuators.
