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Singular LQ Control, Optimal PD Controller and Inadmissible Initial Conditions

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Title Singular LQ Control, Optimal PD Controller and Inadmissible Initial Conditions
 
Creator KALAIMANI, RK
BELUR, MN
CHAKRABORTY, D
 
Subject Cheap control
impulsive solutions
PD controller
singular LQ problem
singular system
transmission zeros
zeros at infinity
SYSTEMS
 
Description We consider a classical control problem: the infinite horizon singular LQ problem, i.e., some inputs are unpenalized in the quadratic performance index. In this case, it is known that the slow dynamics is constrained to be in a proper subspace of the state-space, with the optimal input for the slow dynamics implementable by feedback. In this technical note we show that both the fast dynamics and the slow dynamics can be implemented by a feedback controller. Moreover, we show that the feedback controller cannot be a static feedback controller but can be PD, i.e.,, proportional + differentiate exactly once, in the state. We show that the closed loop system is a singular descriptor state space system and we also characterize the conditions on the system/performance index for existence of inadmissible initial conditions, i.e., initial conditions that cause impulsive solutions. There are no inadmissible initial conditions in the controlled system if and only if in the strictly proper transfer matrix from the unpenalized inputs to the penalized states, there exists at least one maximal minor of relative degree equal to the number of unpenalized inputs. In addition to the above, we prove solvability of the infinite horizon singular LQ problem under milder assumptions than in the literature.
 
Publisher IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
 
Date 2014-10-16T07:11:43Z
2014-10-16T07:11:43Z
2013
 
Type Article
 
Identifier IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 58(10)2603-2608
http://dx.doi.org/10.1109/TAC.2013.2254627
http://dspace.library.iitb.ac.in/jspui/handle/100/15520
 
Language en