Synthesis methods of investigation and control of oscillatory processes in nonlinear dynamical systems

 Methods to improve the reliability and fault diagnosis in complex automated process control systems have identified asa  part of the object of study
The aim of the development of new algorithms is to designated diagnostic and control algorithms, ensuring a high degree of robustness of a closed system with respect to equipment failure,actuators wearness  etc.

Methods of construction and methods of interval observers moving higher order modes have been chosen as the principal methods of synthesis of diagnostic algorithms (observations). Methods of homogeneous systems, implicit functions and Lyapunov stability of the entrance to the state have been selected for the synthesis of control algorithms used . All the results have been published in the top level  (in the field of automatic control) international peer-reviewed journals and conferences.

Within this domain the  following results have been obtained:

1.  Results related to the development of the method of homogeneous systems for the analysis of the robustness and reliability of nonlinear process models, and the expansion of this apparatus to discontinuous system.

2. Applied method of homogeneous systems appling implicit method of Lyapunov functions for the synthesis of the control law that guarantees the convergence of all processes to the desired position of equilibrium within a finite time.

3. Analysis and synthesis of oscillating systems management. The analysis of the properties of robust stability for dynamic systems on manifolds with non-unique equilibrium position or attracting sets.

4. The properties of oscillation by Yakubovich (one of the most common concepts describing oscillatory processes) for hybrid systems have been examined.

5.  Stabilization resonant mode of vibration for robots has been performed. The solution is based on a sliding mode differentiator and speed-gradient method.