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Improper L-infinity Optimal/Suboptimal Controllers

DSpace at IIT Bombay

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Title Improper L-infinity Optimal/Suboptimal Controllers
 
Creator PAL, D
BELUR, MN
 
Subject Dissipative systems
improper transfer function
L-infinity-control
optimal control
polynomial matrix representations
system invariant zeros
QUADRATIC DIFFERENTIAL FORMS
SYSTEMS
 
Description We consider L-infinity-control of MIMO systems and address solvability of the problem over all finite dimensional LTI controllers: i.e., controllers whose transfer functions can be proper or improper. We show that improper controllers are easily dealt with using the behavioral approach, unlike the standard state-space/transfer-matrix methods, and argue that there are cases where an improper controller can outperform a proper controller. In this setting, we next formulate and prove necessary and sufficient conditions for suboptimal L-infinity-control problem solvability and relate this to existing results about system invariant zeros. Further, we infer that in our formulation, assuming suboptimal solvability conditions on the system, an optimal controller always exists, possibly with an improper transfer function. In other words, the infimum L-infinity-norm of the closed loop system is achievable when dealing with both proper and improper controller transfer functions. We illustrate these results through an example for which the optimal L-infinity-controller has an improper transfer function.
 
Publisher IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
 
Date 2014-10-15T13:52:30Z
2014-10-15T13:52:30Z
2012
 
Type Article
 
Identifier IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 57(5)1280-1285
http://dx.doi.org/10.1109/TAC.2012.2191869
http://dspace.library.iitb.ac.in/jspui/handle/100/15033
 
Language en