Indefinite LQ-Problem: The Finite Planning Horizon Case.

摘要

The note considers the problem under which conditions there is, for a discrete-time system, a bounded control that minimizes a general quadratic cost functional. The system considered is linear and has an exogenous component. The cost functional is a quadratic equation over a finite planning horizon with symmetric weighting matrices. It presents necessary and sufficient conditions on these weighting matrices which guarantee the existence of such a bounded optimal control and presents an algorithm to obtain the optimal control. For a special case it derives necessary and sufficient conditions from which a priori it is possible to conclude whether the optimization problem will have a solution for any planning horizon.