Tatiana F. Filippova     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620990; Ural Federal University, 19 Mira str., Ekaterinburg, 620002, Russian Federation)


The nonlinear dynamical control system with uncertainty in initial states and parameters is studied. It is assumed that the dynamic system has a special structure in which the system nonlinearity is due to the presence of quadratic forms in system velocities. The case of combined controls is studied here when both classical measurable control functions and the controls generated by vector measures are allowed.  We present several theoretical schemes and the estimating algorithms allowing to find the upper bounds for reachable sets of the studied control system.   The research develops the techniques of the ellipsoidal calculus and of the theory of evolution equations for set-valued states of dynamical systems having in their description the uncertainty of set-membership kind.  Numerical results of system modeling based on the proposed methods are included.


Control systems, Nonlinearity of quadratic type, Uncertainty, Impulse control, Ellipsoidal calculus, Tube of trajectories

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