Computation of feedback operators for distributed parameter systems with non-normal linearizations

In this paper we consider the problem of computing the functional gains that represent LQR optimal feedback control laws for non-normal linear systems. The problem is motivated by fluid flow control and focuses on the issue of computing functional gains based on linearizations about non-trivial steady flows. Such linearizations lead to non-normal linear dynamic operators and can produce highly sensitivity systems requiring special numerical techniques. Simple examples are presented to illustrate the ideas and to highlight some of the numerical problems. We close with numerical results for a thermal-fluid control problem.