COMPUTATION OF THE DIGITAL LQG REGULATOR AND TRACKER FOR TIME-VARYINGSYSTEMS

Digital optimal control problems, i.e. problems where a continuous-tim e system is controlled by a digital computer, are very often approxima ted by either discrete-time or continuous-time optimal control problem s. A digital controller based on one of these approximations requires a small sampling time and constitutes only an approximate solution. Th e digital LQG regulator and tracker constitute solutions to real digit al control problems which involve sampled-data, piecewise constant con trols and integral criteria. Until now only the numerical computation of the digital LQG regulator in the case of time-invariant system and criterion matrices has been considered in the literature. The control of non-linear stochastic systems about state trajectories is very ofte n performed by an LQG regulator based on the linearized dynamics about the trajectory, which constitute a time-varying system. We present a numerical procedure to compute the digital LQG regulator and tracker i n the case where the system and criterion matrices are time-varying. F inally we present a numerical example.