Summary: Traditional approximate/adaptive dynamic programming (ADP) methods can handle a very special class of systems subject to symmetry constraints. In this study, I extend the exiting ADP to a broader class of nonlinear dynamic systems with asymmetry constraints. Firstly, I propose a novel nonquadratic cost function, based on which the developed optimal controller by solving Hamilton-Jacobi-Bellman equation can limit its value to arbitrarily prescribed bound. Then, to avoid “curse of dimensionality”, I approximately implement the addressed controller via single-network adaptive critic design. Fuzzy hyperbolic model is introduced to construct the single critic network by approximating optimal cost function, from which I further derive the optimal control law. The potential advantages are that the control structure is simple and the computational load is low. Lyapunov synthesis proves the ultimately uniformly bounded stability of closed-loop control system. Finally, numerical simulation results verify the efficiency and superiority of the proposed approach.