Optimal and suboptimal policies for generalized minimum-effort control of second-order systems

This paper discusses optimal and suboptimal control policies which transfer second-order systems to the origin while minimizing some function of control effort
f_{0}^{T}\phi[u(t)]dt
. The time of control
T
is specified only to the extent
T\leq\bar{T}
, where
\bar{T}
is the given upper bound on control time. Control systems with unequal negative real poles are considered. A computational scheme which yields the optimal control policies for these systems is developed, and suboptimal policies are then derived. The effects of suboptimal policies on
f_{0}^{T}\phi[u(t)]dt
are also evaluated.