Km. Grigoriadis et Re. Skelton, ALTERNATING CONVEX PROJECTION METHODS FOR DISCRETE-TIME COVARIANCE CONTROL DESIGN, Journal of optimization theory and applications, 88(2), 1996, pp. 399-432
Citations number
33
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
The problem of designing a controller for a linear, discrete-time syst
em is formulated as a problem of designing an appropriate plant-state
covariance matrix. Closed-loop stability and multiple-output performan
ce constraints are expressed geometrically as requirements that the co
variance matrix lies in the intersection of some specified closed, con
vex sets in the space of symmetric matrices. We solve a covariance fea
sibility problem to determine the existence and compute a covariance m
atrix to satisfy assignability and output-norm performance constraints
. In addition, we can treat a covariance optimization problem to const
ruct an assignable covariance matrix which satisfies output performanc
e constraints and is as close as possible to a given desired covarianc
e. We can also treat inconsistent constraints, where we look for an as
signable covariance which best approximates desired but unachievable o
utput performance objectives; we call this the infeasible covariance o
ptimization problem. All these problems are of a convex nature, and al
ternating convex projection methods are proposed to solve them, exploi
ting the geometric formulation of the problem. To this end, analytical
expressions for the projections onto the covariance assignability and
the output covariance inequality constraint sets are derived. Finally
, the problem of designing low-order dynamic controllers using alterna
ting projections is discussed, and a numerical technique using alterna
ting projections is suggested for a solution, although convergence of
the algorithm is not guaranteed in this case. A control design example
for a fighter aircraft model illustrates the method.