SISO H-Optimal synthesis with initially specified structure of control law

Evgeny I. Veremey; Vladimir V. Eremeev

doi:10.3934/naco.2017009

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2017, Volume 7, Issue 2: 121-138. Doi: 10.3934/naco.2017009

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SISO H-Optimal synthesis with initially specified structure of control law

Evgeny I. Veremey^, and
Vladimir V. Eremeev

Faculty of Applied Mathematics and Control Processes, Saint-Petersburg State University, Saint Petersburg, 199034, Russia

^* Corresponding author: Evgeny I. Veremey
^* Corresponding author: Evgeny I. Veremey

Received: June 2016

Revised: May 2017

Published: October 2017

This article was written based on a study partially supported by the Russian Foundation for Basic Research (RFBR), research project No. 14-07-00083a.

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Abstract

The paper is devoted to particular cases of H-optimization problems for LTI systems with scalar control and external disturbance. The essence of these problems is to find an output feedback optimal controller having initially given structure to attenuate disturbances action with respect to controlled variable and control. An admissible set of controllers can be additionally restricted by the requirement to assign given poles spectrum of the closed-loop system. Specific features of the posed problems are considered and three simple numerical methods of synthesis are proposed to design correspondent H-optimal controllers. To show the simplicity and effectiveness of the proposed approach and the benefits of developed methods, illustrative examples are enclosed to the paper.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Fragment of the surface $J=J(h_{0}, h_{1} )$

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Figure 2. The crossed sections of the surface $J=J(h_{0}, h_{1} )$ for the fixed value of the parameter $h_1$

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