Dubovik S. Asymptotic methods of synthesis of control systems of movement

The object of research are tasks of providing of quality, exactness and stability and methods of their decision. The purpose of research is a development of methods of synthesis of the systems of control, responding to request: closeness in quality to the set simplified standard models; stability to indignations and to inaccuracy in the task of parameters of object of control; simplicity and reliability of realizing algorithms. Research methods is a methods of asymptotic expansions for a singular perturbations differential equations and methods of averaging for nonlinear stochastic differential equations and functional of action. For the linear system submitted in canonical form of singular perturbations, containing parameters of a different infinitesimal degree at derivatives, the task of synthesis by quadratic criterion (LQ-synthesis) is formulated, and carried out the asymptotic analysis of its solution resulting in simplified algorithms of the optimum control. The terminal problem for which the algorithm of optimum control allows to generate feedback in the obvious and simplified kind is separately considered. In a task of LQ-synthesis it is established asymptotic connection of parameters of criterion with reference representations about dynamics of private subsystems. For the maximum permissible size of parameter named in work unstiffness, the estimation resulting in simple algorithms of increase of roughness of a control system is established. On the basis of the received relations and asymptotic estimations methods of composite synthesis of stationary and terminal regulators are developed. Within the framework of the general problem of management by nonlinear system it is developed asymptotic a method of the analysis of the big deviation on a basis functional of actions. It is shown, that rough asymptotic estimation of probability of a critical condition is defined integral quadratic functional on extremal curve of actions. Application of the developed methods in tasks of management by flying devices, for creation of the software of onboard system of an operative estimation of seaworthiness of a vessel is considered and at a choice of parameters of circuits of condenser management of a drive of the high-voltage vacuum switch.