ADAPTIVE OUTPUT CONTROL OF MULTICHANNEL LINEAR STATIONARY SYSTEMS UNDER PARAMETRIC UNCERTAINTY

A. A. Bobtsov, M. V. Faronov, I. B. Furtat, A. A. Pyrkin, J. Wang


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Abstract
The paper deals with the problem of adaptive control for multi-channel linear stationary plants under parametric uncertainty with arbitrary relative degree of each local subsystem. The synthesized regulator provides stabilization of control plant on condition that for each local subsystem only output variables are measured with known relative degrees, but the order of linear differential equations is unknown. We consider the synthesis of control system for two-channel system for simplification of the synthesis method. The "serial compensator" algorithm is chosen as basic approach with A.L. Fradkov's passification theorem and additional filters containing high gain constants in their structure. Durability of the closed system in the group of pointed types of regulators is analyzed and the necessary and sufficient conditions for exponential convergence properties are considered. We suggest adaptive version of the "serial compensator" method from the practical  point of view, where customization of the gain constant is based on the integral type algorithm. We show the results of computer simulation for the third and second order subsystems under parametric uncertainty to illustrate the proposed approach workability. It is shown that the proposed technique makes it possible to synthesize control algorithms for multichannel systems under parametric uncertainty with minimal dynamical order as compared to known foreign and domestic counterparts.

Keywords: adaptive control, multichannel systems, parametric uncertainty

Acknowledgements. The work is partially financially supported by the Government of the Russian Federation (grant 074-U01), Project 14.Z50.31.0031, Government order 2014/190 (project 2118)).

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