Optimal discrete-continuous control for the linear-quadratic regulator problem.

摘要

In the conventional method of discrete-time control, the control-input is held constant across each sampling-interval; i.e., "zero-order hold" type control. In this dissertation a recently introduced generalization of the conventional discrete-time control method, in which the control is allowed to vary with time (open-loop fashion) across each sampling-interval, is considered and applied to the optimal linear-quadratic regulator (LQR) problem. This generalization of discrete-time control, called "discrete-continuous control," leads to significant performance improvements compared to conventional discrete-time control.;An important special case of discrete-continuous control, where control variations are constrained to be linear-in-time across each sampling-interval, is examined in detail and the associated general LQR theory is developed for that special case. The non-inferior performance of the linear-in-time (LiT) D/C control, compared to zero-order hold (ZOH) control, is proved analytically. Necessary and sufficient conditions for superior performance of LiT D/C control are also derived. These latter results are illustrated by two worked numerical examples with simulation plots that clearly demonstrate the LQR performance improvements obtained by (linear-in-time) discrete-continuous control.