In this paper, a new design scheme is presented to solve the optimal control problem for nonlinear systems with unsymmetrical input constraints. This method also relaxes 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. Particularity, the partially-unknown system is investigated and the procedure to obtain the corresponding optimal control policy is introduced. The optimality of the obtained control policy and the stability for the closed-loop dynamics are proved theoretically. Meanwhile, the proposed method in this paper can be further applied to nonlinear control systems whose dynamics are completely known or unknown. Besides, we apply the control design framework proposed in this paper to solve the optimal circumnavigation problem involving a moving target for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our method is compared with that of the existing circumnavigation control law in a numerical simulation and the simulation results validate the effectiveness of our algorithm.
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