The Mathematical Modeling of Nonlinear Dynamical Systems Laboratory was established in 2014
Major fields of research:
- localization of invariant compacts of continuous and discrete dynamical systems, chaotic dynamics;
- research of continuous and discrete nonlinear dynamical systems and management processes based on algebraic and differential-geometric methods and designing of control algorithms for them
- stability research, construction of attraction regions and definition of Lyapunov functions for nonlinear systems;
- investigation of nonminimal phase systems, mathematical modeling of control processes of nonlinear systems;
- geometry of delay systems, systems of integro-differential equations and another type of systems including boundary-differential form;
- calculation of symmetry, integrable symmetries, laws of conservation, dynamical control systems and transormation of such systems and using them in applied research.
- inverse differential operator;
- problem of flatness of dynamical control systems, delay systems and distributed parameters systems;
- the task of wheeled robots yaw;
- designing of advanced spatial maneuvers for aircrafts;
- modeling of laboratory robot`s work using vision systems;
- modeling of spacecraft rotation around its centre of mass;
- modelling of wheeled robot`s behavior under uncertainty;
Most important results achieved by the laboratory staff:
- conditions of asymptotic stability and asymptotic stability in general have been proved in terms of invariant compacts and positively invariant multiplicities;
- trajectories behavior of autonomous and non-autonomous systems of differential equations outside localized multiplicities related to functions have been described;
- functional localization method of invariant compact multiplicities has been extended to families of discrete dynamical systems;
- plotting method of Lyapunov functions for proving the asymptotic stability equilibrium of dynamical systems has been designed;
- functional localization method of invariant compact multiplicities has been extended to differential inclusions
- localization problem of robustly controlled invariant compact multiplicities continuous and discrete dynamical systems with perturbations has been solved.
