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A Linear Quadratic Controller Design Incorporating a Parametric Sensitivity Constraint

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Abstract

The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter variation is handled through an additional quadratic trajectory parametric sensitivity term in the standard LQ criterion to be minimized. The main purpose here is to find a suboptimal linear quadratic control taking explicitly into account the parametric uncertainties. The paper main contribution is threefold: 1) A descriptor system approach is used to show that the underlying singular linear-quadratic optimal control problem leads to a non-standard Riccati equation. 2) A solution to the proposed control problem is then given based on a connection to the so-called Lur’e matrix equations. 3) A synthesis method of multiple parametric SCLQ controllers is proposed to cover the whole parametric uncertainty while degrading as less as possible the intrinsic robustness properties of each local linear quadratic controller. Some examples are presented in order to illustrate the effectiveness of the approach.

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Authors and Affiliations

  1. LUNAM University, Ecole des Mines de Nantes, Nantes, 44307, France

    Mohamed Yagoubi

  2. IRCCyN, UMR CNRS 6597 (Institut de Recherche en Communications et Cyberntique de Nantes), Nantes, France

    Mohamed Yagoubi

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  1. Mohamed Yagoubi
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Correspondence to Mohamed Yagoubi.

Additional information

Recommended by Associate Editor Victor Becerra

Mohamed Yagoubi received M. Sc. degree in automatic control engineering from the Institut National Polytechnique de Grenoble (INPG), France in 1999, and the Ph.D. degree in automatic control from Ecole Centrale de Nantes, France in 2003. In 2004, he was a faculty member at Mines Nantes, France. Currently, he is an associate professor in the Department of Automatic Control, Production and Computer Science at Mines Nantes, France. He has published about 100 refereed journal and conference papers.

His research interests include robust control, LPV systems, descriptor systems, automotive systems, and control theory in general. He is a member of IEEE.

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Yagoubi, M. A Linear Quadratic Controller Design Incorporating a Parametric Sensitivity Constraint. Int. J. Autom. Comput. 16, 553–562 (2019). https://doi.org/10.1007/s11633-016-1048-5

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  • DOI: https://doi.org/10.1007/s11633-016-1048-5

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