On identification of interconnected systems

Objectives. Interconnected control systems are widely used in various technical contexts, generally involving multichannel systems. However, due to the complexity of their description, the problem of identifying interconnected systems has received insufficient attention. As a result, simplified models are commonly used, which do not always reflect the specifics of the object. Thus, the synthesis of mathematical models for the description of interconnected control systems becomes a relevant endeavor. The paper sets out to develop an approach to obtaining models under conditions of incomplete a priori information. A mathematical model is developed on the example of two-channel systems (TCSs) having cross-connections and identical channels. The case of asymmetric cross-connections is considered, along with estimates of their influence on the quality of the adaptive identification system. The problem of estimating the identifiability of the parameters of a TCS is formulated on the basis of available experimental information and subsequent synthesis of the adaptive system. The proposed approach is then generalized to the case of an interconnected system.

Methods. The adaptive system identification and Lyapunov vector function methods are used along with implicit identification representation for the model.

Results. The influence of excitation constancy on estimates of the TCS parameters is demonstrated on the basis of the proposed approach for estimating the identifiability of TCS with cross-connections. The synthesis of adaptive algorithms of parameter estimation for TCSs with cross-connections based on input-output data is generalized to the case of interconnected systems. The results are applied to building models of tracking system and two-channel corrector for automatic control systems.

Conclusions. The features of adaptive identification of TCSs with identical channels, cross-connections and feedbacks are considered. The conditions for the TCS identifiability are obtained. Adaptive algorithms for estimating TCS parameters are synthesized. The proposed approach is generalized to the case of nonidentical channels and multi-connected systems. The exponential dissipativity of the adaptive identification system is verified. The proposed methods can be used in the development of systems for identification and control of complex dynamic systems.

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