Paper Info
Title
Optimal control of stable weakly regular linear systems.
Abstract
The paper extends quadratic optimal control theory to weakly regular linear systems, a rather broad class of infinite-dimensional systems with unbounded control and observation operators. We assume that the system is stable (in a sense to be defined) and that the associated Popov function is bounded from below. We study the properties of the optimally controlled system, of the optimal cost operatorX, and the various Riccati equations which are satisfied byX. We introduce the concept of an optimal state feedback operator, which is an observation operator for the open-loop system, and which produces the optimal feedback system when its output is connected to the input of the system. We show that if the spectral factors of the Popov function are regular, then a (unique) optimal state feedback operator exists, and we give its formula in terms ofX. Most of the formulas are quite reminiscent of the classical formulas from the finite-dimensional theory. However, an unexpected factor appears both in the formula of the optimal state feedback operator as well as in the main Riccati equation. We apply our theory to an extensive example.
Year
DOI
Venue
1997
10.1007/BF01211550
MCSS
Keywords
Field
DocType
spectral factorization,optimal control,feedback system,linear system,control theory,riccati equation,satisfiability,quadratic optimization
Optimal control,Linear-quadratic-Gaussian control,Linear system,Control theory,Operator (computer programming),Riccati equation,Linear-quadratic regulator,Mathematics,Discrete system,Bounded function
Journal
Volume
Issue
ISSN
10
4
1435-568X
Citations 
PageRank 
References 
28
7.92
5
Authors
2
Name
Order
Citations
PageRank
Martin Weiss1287.92
George Weiss231664.49