Square Indefinite LQ-Problem: Existence of a Unique Solution

摘要

In this paper, we consider discrete-time systems, We study conditions under which there isa unique control that minimizes a general quadratic cost functional. The system considered is described by a linear time-invariant recurrence equation in which the number of inputs equals tlie number of states. The cost functional differs from the usual one considered in optimal control theory, in the sense that we do not assume that the weight matrices considered are semipositive definite. For both n finite planning horizon and an infinite horizon, necessary and sufficient solvability conditions are given. Furthermore, necessary and sufficient conditions are derived for the existence of a solution for an arbitrary finite planning horizon.