Design algorithms for a sensitivity constrained suboptimal regulator

The problem of finding the linear feedback control comprised of state and trajectory sensitivity terms which minimizes an infinite-time quadratic cost functional containing sensitivity variables is discussed. Since trajectory sensitivity cannot be accurately modelled in a closed-loop formulation the control feeds back approximate sensitivity terms. As the minimizing control is dependent on initial conditions, necessary conditions for a minimum are derived which satisfy various alternative sets of initial condition criteria. An efficient computer algorithm, based on a gradient search technique, is proposed for finding the feedback gains. By means of a numerical example it is shown that it is possible to reduce trajectory sensitivity while retaining certain desirable features of the linear optimal regulator design. Finally an algorithm is suggested for finding the linear feedback control comprised of state terms alone which minimizes the augmented cost functional.