The LQ controller problem: an example

Abstract

We provide an example of LQ controller synthesis for a distributed plant, namely an RLCG transimssion line without distortion. The characteristic feature of our example is that both control and observation are of houndary form, and thus this example is beyond the scope of the existing theory for the LQ problem. The formal spectral-factorization method is used to get an explicit analytic form of the optimal controller. It is shown that this control law has an extremely simple physical realization. The formally derived optimal controller is then confirmed by the Wiener-Hopf technique. Our example shows the need for some generalization of the existing LQ-problem theory as well as the spectral-factorization method.