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Composite control of nonlinear singularly perturbed systems via approximate feedback linearization

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Abstract

This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed (SP) system using approximate feedback linearization (AFL) method. The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system. According to AFL approach, we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately. The resulting AFL control is constructed in the form of asymptotic composition (composite control). Standard procedure for the composite control design consists of the following steps: 1) system decomposition, 2) solution of control problem for fast subsystem, 3) solution of control problem for slow subsystem, 4) construction of the resulting control in the form of the composition of slow and fast controls. The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system. To overcome this, we propose to change the sequence of the design procedure: 1) solving the control problem for fast state variables part, 2) system decomposition, 3) solving the control problem for slow state variables part, 4) construction of the resulting composite control. By this way, fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable. The application of the proposed approach is illustrated through several examples.

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This work was supported by Russian Foundation for Basic Research (No. 15-08-06859a) and by the Ministry of Education and Science of the Russian Federation in the framework of the basic part of the state order (No. 2.8629.2017).

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Authors and Affiliations

  1. Sevastopol State University, Sevastopol, 299053, Russian Federation

    Aleksey Kabanov & Vasiliy Alchakov

Authors
  1. Aleksey Kabanov
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  2. Vasiliy Alchakov
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Correspondence to Aleksey Kabanov.

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Recommended by Associate Editor Zheng-Tao Ding

Aleksey Kabanov received the Ph.D. degree in systems and processes of control from the Sevastopol National Technical University, Ukraine in 2012. He is currently an associate professor of Department of Informatics and Control in Technical Systems, Sevastopol State University, Ukraine.

His research interests include autonomous vehicle control (aerial unmanned vehicles, mobile robotics, etc), singular perturbation theory and methods in control problems, robust and adaptive control, and intelligent control systems.

Vasiliy Alchakov received the Ph.D. degree in systems and processes of control from the Sevastopol National Technical University, Ukraine in 2013. He is currently an associate professor of Department of Informatics and Control in Technical Systems, Sevastopol State University, Ukraine.

His research interests include data mining, terminal and adaptive control, process modeling and simulations for optimization of operating processes.

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Kabanov, A., Alchakov, V. Composite control of nonlinear singularly perturbed systems via approximate feedback linearization. Int. J. Autom. Comput. 17, 610–620 (2020). https://doi.org/10.1007/s11633-017-1076-9

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