NDLI: Fixed-Order H-Infinity Control for Interconnected Systems Using Delay Differential Algebraic Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Gumussoy, Suat Michiels, Wim
Copyright Year	2011
Abstract	We analyze and design H-infinity controllers for general time-delay systems with time-delays in systems' state, inputs, and outputs. We allow the designer to choose the order of the controller and to introduce constant time-delays into the controller. The closed-loop system of the plant and the controller is modeled by a system of delay differential algebraic equations (DDAEs). The advantage of the DDAE modeling framework is that any interconnection of systems and controllers prone to various types of delays can be dealt with in a systematic way, without using any elimination technique. We present a predictor-corrector algorithm for the H-infinity norm computation of systems described by DDAEs. Instrumental to this we analyze the properties of the H-infinity norm. In particular, we illustrate that it may be sensitive with respect to arbitrarily small delay perturbations. Due to this sensitivity, we introduce the strong H-infinity norm, which explicitly takes into account small delay perturbations, inevitable in any practical control application. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs. Using this algorithm and the computation of the gradient of the strong H-infinity norm with respect to the controller parameters, we minimize the strong H-infinity norm of the closed-loop system based on nonsmooth, nonconvex optimization methods. By this approach, we tune the controller parameters and design H-infinity controllers with a prescribed order or structure.
Starting Page	2212
Ending Page	2238
Page Count	27
File Format	PDF
ISSN	03630129
DOI	10.1137/100816444
e-ISSN	10957138
Issue Number	5
Volume Number	49
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-10-27
Access Restriction	Subscribed
Subject Keyword	$H^\infty$-control time-delay systems Applications in optimization, convex analysis, mathematical programming, economics Methods for differential-algebraic equations H-infinity delay differential algebraic equations interconnected systems fixed-order controller
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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