A Theory of Optimally and Suboptimally Controlled Linear Systems

摘要

The optimal open loop control policy of a linear discrete deterministic system with respect to an additive quadratic cost functional is derived. Proportional feedback control is postulated and the system is optimized with respect to the same cost functional by choice of reference variables. Necessary and sufficient conditions on the feedback matrix in order that this optimization is equivalent to the open loop optimization are presented. The conditions on the feedback matrix are assumed not to be fulfilled and sufficient conditions for the existence of an optimizing procedure are presented. This procedure is exhibited and shown to result in a nonunique best policy and a sub-optimal cost (compared to the open loop optimal control). A second type of suboptimality, that of time selection of control variables, is investigated. (Author)