Paper Info
Title
Optimal control of systems with a unitary semigroup and with colocated control and observation
Abstract
We solve the quadratic optimal control problem on an infinite time interval for a class of linear systems whose state space is a Hilbert space and whose operator semigroup is unitary. The difficulty is that the systems in this class, having unbounded control and observation operators, may be ill-posed. We show that there is a surprisingly simple solution to the problem (the optimal feedback turns out to be output feedback). Our approach is to use a change of variables which transforms the system into a one which, according to recent research, is known to be conservative. We show that, under a mild assumption, the transfer function of this conservative system is inner, and then it follows that the optimal control of this conservative system is trivial. We give an example with the wave equation on an n-dimensional domain, with Neumann control and Dirichlet observation of the velocity.
Year
DOI
Venue
2003
10.1016/S0167-6911(02)00276-1
Systems & Control Letters
Keywords
Field
DocType
Semigroup of unitary operators,Colocated control and observation,Conservative linear system,Quadratic optimal control,Unbounded control and observation operators,Output feedback,Riccati equation
Change of variables,Hilbert space,Mathematical optimization,Optimal control,Linear-quadratic-Gaussian control,Linear system,Control theory,Riccati equation,Semigroup,State space,Mathematics
Journal
Volume
Issue
ISSN
48
3
0167-6911
Citations 
PageRank 
References 
6
1.45
4
Authors
1
Name
Order
Citations
PageRank
George Weiss131664.49