Issue 3 (197), article 3

DOI:https://doi.org/10.15407/kvt197.03.033

Cybernetics and Computer Engineering, 2019, 3(197), pp.

Zhiteckii L.S.1, PhD (Engineering),
Acting Head of the Intelligent Automatic Systems Department
e-mail: leonid_zhiteckii@i.ua

Azarskov V.N.2, DSc. (Engineering), Professor,
Chief of the Aerospace Control Systems Department,
e-mail: azarskov@nau.edu.ua

Solovchuk K.Y.3,
Assistant of the Department of Computer Information Technologies and Systems
e-mail: solovchuk_ok@ukr.net

1International Research and Training Center for Information Technologies
and Systems of the National Academy of Sciences of Ukraine
and Ministry of Education and Science of Ukraine,
40, Acad. Glushkov av., Kyiv, 03187, Ukraine

2National Aviation University, Kyiv, Ukraine.
1, Kosm. Komarova av., Kyiv, 03680, Ukraine

3Poltava National Technical Yuri Kondratyuk University, Poltava, Ukraine.
24, Pershotravneva av., Poltava, 36011, Ukraine

SOLVING A PROBLEM OF ADAPTIVE STABILIZATION FOR SOME STATIC MIMO SYSTEMS

Introduction. The adaptive stabilization of some classes of uncertain multivariable static plants with arbitrary unmeasurable bounded disturbances is addressed in this article. The cases where the number of the control inputs does not exceed the number of the outputs are studied. It is assumed that the plant parameters defining the elements of its gain matrix are unknown. Again, the rank of this matrix may be arbitrary. Meanwhile, bounds on external disturbances are supposed to be known. The problem stated and solved in this work is to design adaptive controllers to be able to ensure the boundedness of the all input and output system’s signals in the presence of parameter uncertainties.

The purpose of this article is to show that it is possible to stabilize any uncertain multivariable static plant which gain matrix may be either square or nonsquare and may have an arbitrary rank remaining unknown for the designer.

Methods. The methods based on recursive point estimation of unknown plant parameters are utilized to design the adaptive inverse model-based controller.

Results. The asymptotic properties of the adaptive controllers have been established. Simulation results have been presented to support the theoretic studies.

Conclusion. The adaptive control laws proposed in this article can guarantee the boundedness of all the signals generated by the feedback control systems. However, this important feature will achieve via an “overparameterization” of these systems. Nevertheless, the simulation experiments demonstrate their efficiency.

Keywords: adaptive control, boundedness, discrete time, estimation algorithm, feedback, multivariable system, uncertainty.

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Received 30.05.2019