Use of the Method of Guidance by a Required Velocity in Control of Spacecraft Attitude

We apply the method of guidance by a required velocity for solving the optimal control problem over spacecraft’s reorientation from known initial attitude into a required final attitude. We suppose that attitude control is carried out by impulse jet engines. For optimization of fuel consumption, the controlling moments are calculated and formed according to the method of free trajectories together with principle of iterative control using the quaternions for generating commands to actuators. Optimal solution corresponds to the principle “acceleration - free rotation - separate corrections - free rotation - braking”. Rotation along a hitting trajectory is supported by insignificant correction of the uncontrolled motion at discrete instants between segments of acceleration and braking. Various strategies of forming the correction impulses during stage of free motion are suggested. Improving accuracy of achievement of spacecraft's final position is reached by terminal control using information about current attitude and angular velocity measurements for determining an instant of beginning of braking (condition for start of braking based on actual motion parameters is formulated in analytical form). The described method is universal and invariant relative to moments of inertia. Developed laws of attitude control concern the algorithms with prognostic model, the synthesized control modes are invariant with respect to both external perturbations and parametric errors. Results of mathematical modeling are presented that demonstrate practical feasibility and high efficiency of designed algorithms

О двойственности для пространств голоморфных функций конечного порядка роста

We describe the strong dual space (Os(D)) for the space Os(D) = Hs(D) \ O(D) of holo- morphic functions from the Sobolev space Hs(D), s 2 Z, over a bounded simply connected plane domain D with infinitely differential boundary @D. We identify the dual space with the space of holomorhic functions on Cn nD that belong to H1�����s(GnD) for any bounded domain G, containing the compact D, and vanish at the infinity. As a corollary, we obtain a description of the strong dual space (OF (D)) for the space OF (D) of holomorphic functions of finite order of growth in D (here, OF (D) is endowed with the inductive limit topology with respect to the family of spaces Os(D), s 2 Z). In this way we extend the classical Grothendieck–K¨othe–Sebasti˜ao e Silva duality for the space of holomorphic functionsМы описываем сильное сопряженное пространство (Os(D)) для пространства Os(D) = Hs(D) \ O(D) голоморфных функций из пространства Соболева Hs(D), s 2 Z, над ограниченной односвязной плоской областью D с бесконечной гладкой границей @D. Мы идентифицируем сопряженное пространство как пространство голоморфных функций на Cn nD, которые принадлежат H1s(G n D) для любой ограниченной области G, содержащей компакт D, и равны нулю в бесконечности. Как следствие, мы получаем описание сильного сопряженного пространства для пространства OF (D) голоморфных функций конечного порядка роста в D (здесь, OF (D) снабжено топологией индуктивного предела относительно семейства пространств Os(D) голоморфных соболевских функций, s 2 Z). Таким образом, мы обобщаем классическую двойственность Гротендика–К¨ете–Себастиана и Сильвы для голоморфных функци