Alternating convex projection methods for covariance control design

Abstract

The problem of designing a static state feedback or full order dynamic controller is formulated as a problem of designing an appropriate plant state covariance matrix. We show that closed loop stability and multiple output norm constraints imply that the plant state covariance matrix 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 address the covariance optimization problem to construct an assignable covariance matrix which satisfies output performance constraints and is as close as possible to a given desired covariance. We also treat inconsistent constraints where we look for an assignable covariance matrix which ‘best’ approximates desired but non-achievable output performance objectives (we call this the infeasible covariance optimization problem). All these problems are of a conve...