| Abstract: | For a selected family of Lagrange-type control problems involving a nonnegative integral costJ
T
(y,u) over the interval 0,T], 0<T< , with system conditions consisting of differential inequalities and/or equalities, the following material is treated: (i) a resumé of relevant necessary conditions and sufficient conditions for a pair (y
T
,u
T
) to minimizeJ
T
(y,u); (ii) conditions sufficient for the convergence asT of minimizing pairs (y
T
,u
T
) over 0,T] to a limit pair (y
,u
) over the infinite-time interval 0, ); (iii) conditions sufficient for (y
,u
) to minimize the costJ
(y,u) over 0, ); and (iv) conditions sufficient for the optimal cost per unit timeJ
T
(y
T
,u
T
)/T to have a limit asT. |
