Shushlyapin E. Models of terminal state and their using for the problems of analysis and syntheses of control systems

The object of study are control systems’ functional dynamic models. The purpose of the study is to develop a new functional dynamic models’ class of linear and nonlinear multivariate systems as well as built on their base functional forms of optimum and terminal control methods, of sensitivity analysis and covariance analysis. Methods of research are the following: mathematical analysis based on differential and integral calculuses, matrix algebra, theories of chances and mathematical statistics, optimum control theory, autocontrol theory, theory of electrical machines and devices, hydromechanics; there was also used a computer modeling with the help of modern automation programming systems and simulation modeling packages. A new facility for descripting terminal dynamic differential system is detrmined in the study. And it is named the «model of terminal state». Models of terminal state are built on the base of transitional matrixes and so called variables of terminal state. This variableshave the sense of predicted values of terminal state for uncontrolled moving of a system with a some condition at a certain moment. Models of terminal state are determined for linear continuous systems, linear continuous systems with solution breakups in given moments of time, nonlinear ones with differentiated nonlinearities. All the systems have additive control and may have additional algebraic restrictions. Herewith a determination of transitional matrix for a nonlinear system and the way of its calculating by the model of state for the differential systems with additional controlling influences derived by V.M Alexeev were used. Such new methods as the method of optimum control and terminal state’s sensitivity analysis for linear non-stationary systems and the method of terminal control and covariance analysis for multivariate nonlinear differential systems with smooth nonlinearities were designed on the base of terminal state model’s application. All suggested methods are carried to numerical algorithmsand computer programs. The method of terminal control named «method of terminal state» was theoretically investigated and tested by computer modeling on the problems of controlling eleven multivariable objects taken from different spheres of human activity such as elecrric power engineering, hydromechanics, management, chemical kinetics and moving object control.