Development of new methods of adaptive control of linear and nonlinear dynamical systems under external disturbances and unrecorded dynamics

Formally, the study can be divided into three main sections :

analysis of the problem of managing complex dynamic systems
development of methods of nonlinear and adaptive control of complex systems ,
experimental research and testing methods obtained .

Due to  the current understanding of the breadth of nonlinear processes and complex systems is not always possible to impose restrictions on the class of objects , in the framework of the research , along with the basic features of complex systems (including parametric and functional uncertainty of the object and its environment functioning perturbation dynamics and unrecorded ) , and act not a few other important factors related to ensuring the robustness and reliability , taking into account the saturation delay , networking, oscillations and bifurcations , as well as providing quality performance of a complex system.

Block 1 .

1. Development of algorithms and study of the stability of nonlinear control systems with saturation and delay

As part of the research unit  the following objectives have been identified:

Determination of  the parameters of the system and / or external influences under which arise in the system globally asymptotically stable oscillations , ie the system tends to a steady ( limit ) solution, which does not depend on the initial conditions.
Characterisation of the steady solutions (limiting fluctuations ) of claim 1, to assess the quality of control in a closed system.

As a method of investigating on the stability of selecteda  traditional method based on Lyapunov functions has ben chosen , and to estimate the parameters of steady solutions harmonic balance method has been applied.  The accuracy and range of applicability of the method garmonic balance is being determined  based on the approach that is close to the method of Lyapunov functions.

Block 2 .

2 . Interval observations for nonlinear objects

The objective of the research is to develop new synthesis algorithms interval observers and control algorithms , providing a high degree of robustness of a closed system with respect to the signal and parametric uncertainty.

Block 3 .

1.3 Ensuring the reliability and faults resistance  of complex dynamic systems

The purpose of this unit is to develop new diagnostic algorithms and control algorithms , providing a high degree of robustness of a closed system with respect to equipment failure , wear actuators etc. Object of study of this research unit are methods to improve the reliability tand fault diagnosis in complex automated process control systems . As the main methods of synthesis of diagnostic algorithms (observations )methods of construction and methods of interval observers moving higher order modes have been chosen . Homogeneous systems and sustainability of the entrance to the state  have been used to control algorithms synthesis methods.