On the identification of decentralized systems

Objectives. The work set out to consider the problem of identification of decentralized systems (DS). Due to the increasing complexity of systems and a priori uncertainty, it becomes necessary to identify appropriate approaches and methods. In particular, this concerns the parametric identifiability (PI) of DSs. This condition can be explained in terms of the complexity of the DS and the presence of internal relationships that complicates the process of parametric estimation. Thus it becomes necessary to propose an approach to PI based on meeting the conditions of the excitation constancy that takes subsystem relationships into account. A class of nonlinear DS is considered whose nonlinearities satisfy the sectoral condition. By taking this condition into account a more rational approach can be taken to the analysis of the DS properties. The work additionally set out to: (1) develop an approach to the analysis of the properties of adaptive identification systems (AIS), taking into account the requirements for the quality of the processes and synthesis of adaptive parametric algorithms; (2) investigate the possibility of using signal adaptation algorithms in DS identification systems and searching for a class of Lyapunov functions for the analysis of AIS with such algorithms; (3) model the proposed methods and algorithms in order to confirm the results obtained.

Methods. The research is based on adaptive identification, implicit identification representation, S-synchronization of a nonlinear system, sector condition, and Lyapunov vector function methods.

Results. The conditions for the parametric identifiability of the DS at the output and in the state space are obtained. A criterion is proposed for estimating the stability of an AIS with signal adaptation. Algorithms for adjusting the parameters of an AIS are synthesized. The exponential dissipativity of the evaluation system is confirmed. The influence of interrelations in the subsystems on the properties of the obtained parameter estimates is considered. An adaptive algorithm can be described by a dynamic matrix system if a functional constraint is imposed on the AIS. The proposed methods and algorithms are modeled to confirm their validity.

 Conclusions. Considering the problem of identifying nonlinear DS under uncertainty, estimates have been obtained for the nonlinear part of the system satisfying the quadratic condition. The parametric identifiability of nonlinear DS has been confirmed. Algorithms for parametric and signal adaptive identification have been synthesized. A class of Lyapunov functions is proposed for evaluating the properties of an adaptive system with signal adaptation. The exponential dissipativity of processes in an adaptive system is demonstrated.

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