  In this paper, a novel design scheme is introduced to solve the optimal
control problem for nonlinear systems with unsymmetrical and state-dependent
input constraints. By introducing an initial stabilizing control policy as the
baseline of the constructed optimal control policy, we remove the assumption in
the current study for the adaptive optimal control, that is, the internal
dynamics should hold zero when the state of the system is in the origin.
Particularly, nonlinear control systems with partially-unknown dynamics are
investigated and the procedure to acquire the corresponding optimal control
policy is presented. The stability for the closed-loop dynamics and the
optimality of the obtained control policy are both proved. Besides, we apply
the proposed control design framework to solve the optimal circumnavigation
problem based on the accumulative Fisher information for a fixed-wing unmanned
aerial vehicle (UAV). The control performance of our algorithm is compared with
that of the existing circumnavigation control policy in a numerical simulation.
