G.G.Vokin

Research Institute of Space Systems

Khrunichev State Space Research-Production Center

Jubilejny, Moscow Region, 141091, Russia

The necessity of securing both of a high exactitude of motion of center of masses and about it of space-rocket objects (missiles, war heads, small space vehicles, accelerating units, space stations and other similar objects), especially in conditions of intensive disturbances, process variation or even some failures, induces to search for controls synthesis methods that ensure increased values of response and a dynamic exactitude of stabilization systems.

The analysis of known methods of synthesis of optimum systems comes to conclusion, that their realization aboard meets a serious engineering difficulties connected, in particular, to necessity of large speed of computing devices, as, becoming already conventional, the variational tasks on searching optimum controls and parameters are reduced in important cases actually to other not less difficult tasks, in particular, to searching of entry conditions of the conjugate systems, evaluation of uncertain factors or to solution of partial equations. As it will be shown in the article, the mentioned difficulties substantially are eliminated on paths of construction of optimum controls synthesis algorithms based on existence of strong connection between system stability and optimality. It allows for the first time in practical important cases to discover optimum controls as explicit functions only of natural phase coordinates, and irrespective of system dimension. It is necessary to note, that though the work was carried out some years ago as a part of confidential research, however, it remains, in opinion of the author, a methodical magnitude till now and can form the basis for further researches and practical applications in the field of development of stabilization systems of various control objects, including air and aerospace objects.

NOTATIONS:

1. In the work, a mathematical relation of Lyapunov second method and optimality conditions of dynamic processes is determined in an explicit aspect. The appropriate theorems justifying the methodical approach to synthesis of optimum controls and detecting properties of optimum-steady automatic systems of stabilization are proved. Based on the determined connection, the new methods of synthesis of optimum controls are developed, and the properties of synthesizing optimum-steady system of stabilization are investigated. It is proved, that under system optimization by integrated functional, which element of integrations are positive definite functions of phase coordinates, in a system the properties of small sensitivity to parameter variations increase, the ε-autonomy and ε-invariance attain, and both dynamic exactitude and speed essentially improve under intensive constant perturbations.

2. The new method of synthesis (method of coincident directions), being a basis of optimum controls synthesis algorithms is offered. The advantages of the method in comparison with known variational methods of controls synthesis is:

─ possibility of solution (analytical or numerical) linear and nonlinear tasks of controls synthesis with only natural phase coordinates use;

─ no need to search of some auxiliary variable values (e.g., initial conditions of adjoin system, uncertain multipliers), as a rule, by enumeration of their values;

─ essential drop of the requirements to performance and size of memory of on-board computing devices.

3. When the obtained algorithms of synthesis of optimum controls use:

─ ensures a high dynamic exactitude and speed of stabilization systems in conditions of intensive perturbations and variations of parameters;

─ increases upper bounds of admissible perturbations and variations of parameters, at which the system keeps acceptable dynamic characteristics, that under action of intensive perturbations can decrease, e.g., radius of field of perturbation source, in which the space-rocket vehicles loses a stability under action, e.g., of power loads.

The offered methods of synthesis of controls are realizable technically onboard the mentioned vehicles and finally can ensure raise of an exactitude of control of their movement under conditions of intensive perturbations of various physical nature.