MAXIMAL GUARANTEED ACCURACY OF A BANG-BANG REGULATOR IN A ONE-DIMENSIONAL STABILIZATION PROBLEM

The problem of [he determination of an optimal bang-bang control of a one-dimensional dynamical model for the worst constrained disturbance is considered. It can be applied, for example, to the stabilization of the angular motion of spacecraft on-off jet engines with delayed thrust cutting-off. By using the phase plane method and the theory of differential games [1-3], we investigate the potentials for the transfer of the system from an arbitrary initial state lo a mode of motion with the minimal (with respect to all initial states and all admissible controls) guaranteed error of stabilization. The solution is presented for a domain in the space of parameters of the problem in question. In [4-6], bang-bang control laws were considered that could be effectively applied lo the stabilization of motion. In [3], game problems of dynamics were studied for [he case of constraint disturbances but without a delay of the control. The results of the investigation of a number of minimax. problems with delay of the control, obtained by (he authors of the present paper, were published in [7, pp. 253-270]. In particular, in the cited paper, the solution of a simplified version of the problem treated in the present paper was given.