LAUSR

Abstract This paper addresses approximate optimal stabilization problems for nonlinear systems in the presence of mismatched external disturbances via asymptotically stable critic designs. By establishing the nonlinear disturbance observer, the corresponding information is utilized to construct the online updated cost function, which reflects the real-time disturbances, regulation and control simultaneously. With the help of the proper cost function, the Hamilton–Jacobi–Bellman equation is solved by employing a critic neural network, whose weight vector is guaranteed to be asymptotically stable with nested tuning laws. The approximate optimal control is derived to guarantee the closed-loop system to be ultimately uniformly bounded based on the Lyapunov stability theorem. The effectiveness of the developed stabilization scheme is verified via simulations of two numerical examples.