On the theoretical sub-optimality of optimal disturbance-utilizing control laws

Optimal control problems involve uncertain external disturbances w(t) and/or set-point/servo-commands y_c (t). The authors consider a class of a linear-quadratic set-point problems with disturbances and use a reverse-time solution procedure introduced by Kalman to solve the absolute optimal control under the idealistic case that at each time t the future behaviors of y_c(t) and w(t) are completely known a priori. An alternative optimal control is also developed using the optimal disturbance-utilizing control (DUC) theory in which future behaviors of {y_c(t), w(t)} are not known but, rather, sparse-impulse driven state-models of y_c(t) and w(t) are introduced. The general similarities and differences in the two optimal controls are discussed and specific versions of those controls are derived for a concrete example. Optimal DUC control is apparently the best of all rational physically realizable controls for the class of problems considered