A note on finite-horizon LQ problems with indefinite cost - Ferrante, A.; Ntogramatzidis, Lorenzo (Pergamon Press, 2015)
This paper addresses the discrete-time finite-horizon linear quadratic (LQ) optimal control problem in the case in which the quadratic forms in the performance index are not assumed to be positive semidefinite, but only symmetric. We provide a necessary and sufficient condition for the existence of an optimal control.