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Information × Registration Number 0210U001004, 0109U007024 , R & D reports Title Stabilization problems for hybrid dynamical systems with control popup.stage_title Head Zuyev Alexander Leonidovich, Registration Date 12-01-2010 Organization Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine popup.description2 Object of investigation: hybrid dynamical systems described by a set of equations with discrete time and differential equations, of systems of ordinary and partial differential equations, as well as by equations in abstract functional spaces. Goal of investigation: developments of method for the stabilization of a wide class of hybrid systems. Methods of investigation: direct Lyapunov method, methods of impulse systems theory, methods of semigroups of operators. Results and novelty: the asymptotic stability problem of an unperturbed motion is investigated for a hybrid mechanical system consisting of absolutely rigid and flexible elements with taking into account the potential forces of gravity and elastic deformations. The stabilization problem is considered for such a model with a control in the right hand side of the partial differential equation of motion and in the boundary conditions. A control functional is obtained for the case of mechanical system that contains the elastic element as a beam with two moving ends. The stabilization problem of equilibrium is considered for nonlinear control system under the assumption that the set of control values is a polyhedron. In a model case, sufficient stabilizability conditions are obtained. The problem of stabilization of a mathematical pendulum with moving suspension point is considered around an inclined position that generalizes the Kapitsa problem. For solving such a problem, the possibility of applying standard and impulse control at the suspension point is studied. It is proved that, for any bounded motion of the suspension, the exact equilibriums are vertical positions. Controls ensuring periodical motions of the suspension point and harmonic oscillations of the pendulum around a fixed inclined position are constructed. The stability of such a motion is investigated. Fields of application: mathematical control theory, mechanics of distributed parameter systems, impulse control. Product Description popup.authors Зуєв Олександр Леонідович Неспірний Віталій Миколайович popup.nrat_date 2020-04-02 Close