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Information × Registration Number 0210U000460, 0108U004830 , R & D reports Title Control of dynamical systems under uncertainties and perturbations popup.stage_title Head Kuntsevich Vsevolod Mykhailovich, Registration Date 16-02-2010 Organization Space Research Institute popup.description2 The investigation object is methods and algorithms used for estimation of the state and parameters of dynamic systems and synthesis of their control under uncertainty of their properties, properties of noise and external disturbances. The aim of the work consists in the development of robust methods and algorithms for estimation of the state and parameters of dynamic systems and methods of synthesis of their robust control on the basis of the guaranteed approach to the mathematical interpretation of uncertainties without using assumptions about their probability nature. The investigation methods are methods of linear algebra, set theory, convex analysis, optimization and mathematical programming, methods of estimation and control under uncertainty conditions, computer modelling. A constructive method of synthesis of robustly stable control systems for nonlinear nonstationary objects using the minimization condition of the Lyapunov function first difference is developed. A method of finite-dimensional approximation of mathematical models of distributed systems is proposed, i.e. a method of approximation of partial differential equations by usual differential equations. A new approach to solving problems of state estimation of nonlinear continuous and discrete systems on the basis of incomplete measurements at a sliding interval is developed. A generalized conception of robust dissipativity of discrete systems is introduced and its properties are investigated with the help of the Lyapunov functions method. It is shown that the use of the sequence of Lyapunov function sets allows one to improve the initial estimate of the limiting set of a dissipative system. The method of interval (set) analysis is applied to the study of interval statistical characteristics of indefinite sequences. New robust methods of ellipsoidal estimation of the state vector of linear and nonlinear dynamic systems on the basis of current measurements of their outputs distorted by additive noise are proposed. In contrast to the known algorithms that take into account only the finiteness of noise, these methods additionally take into account the finiteness of the rate of their variation. The efficiency of using the proposed methods in a closed control contour is illustrated by the example of computer modelling of the attitude control system of a space vehicle. New results are obtained in the solution of the interdisciplinary problem of determination of invariant sets of discrete dynamic systems subjected to uncontrolled finite disturbances. A method for obtaining upper bounds of the invariant sets of nonstationary linear and some classes of nonlinear discrete systems is developed. A constructive method of solving the problem of robust control synthesis for a family of nonlinear nonstationary objects with uncontrolled disturbances using the minimization condition of the invariant set radius is proposed. The computer modelling illustrated the efficiency of the proposed method. An estimation method using incomplete and inaccurate measurements of the full state vector of an object and parameters of its model at a sliding interval is proposed and developed. A method of iterative structural-parametric identification of multidimensional discrete linear systems using data with limited uncertainty is developed. Both systems with scalar input and output and cases of multiply connected systems with multiple channels of measurements and input influences are considered. Product Description popup.authors Волосов Віктор Вікторович Губарев В'ячеслав Федорович Жуков Олексій Олегович Кунцевич Всеволод Михайлович Личак Михайло Михайлович Лубенець Марія Олександрівна Максимюк Любов Володимирівна Царук Ніна Петрівна Шевченко Володимир Миколайович popup.nrat_date 2020-04-02 Close