Аннотация:The problem of linear-quadratic optimal terminal control of a linear discretedynamic system with a vector input is considered. Solutions of the problem based on theapparatus of the optimization form of pseudo-circulation of matrices are given. The solution ofthe optimal terminal control problem is obtained, which ensures the achievement of theterminal control goal and the passage of the trajectory of the system as close as possible to thespecified intermediate points. A complete set of solutions to the problem of optimal terminalcontrol of a bundle of trajectories is obtained.