Km. Grigoriadis et Re. Skelton, ALTERNATING CONVEX PROJECTION METHODS FOR COVARIANCE CONTROL DESIGN, International Journal of Control, 60(6), 1994, pp. 1083-1106
Citations number
29
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control
The problem of designing a static state feedback of full order dynamic
controller is formulated as a problem of designing an appropriate pla
nt state covariance matrix. We show that closed loop stability and mul
tiple output norm constraints imply that the plant state covariance ma
trix lies at the intersection of some specified closed convex sets in
the space of symmetric matrices. We address the covariance feasibility
problem to determine the existence and compute a covariance matrix to
satisfy assignability and output norm performance constraints. We add
ress the covariance optimization problem to construct an assignable co
variance matrix which satisfies output performance constraints and is
as close as possible to a given desired covariance. We also treat inco
nsistent constraints where we look for an assignable covariance matrix
which 'best' approximates desired but non-achievable output performan
ce objectives (we call this the infeasible covariance optimization pro
blem). All these problems are of a convex nature and alternating conve
x projection methodologies are suggested to solve them. These techniqu
es provide simple and effective numerical algorithms for a solution of
non-smooth convex programs and their presentation in this paper is of
particular importance since (to the authors' knowledge) this is the f
irst time these methods have been used in control design, and they mig
ht find wide applicability in several aspects of computational control
problems. Expressions for the required convex projections on the assi
gnability and the performance constraint sets are derived. An example
illustrates the methodology.