Correction to: Adaptive asymptotic stabilization of uncertain nonstrict feedback nonlinear HOFA systems with time delays

We consider the adaptive control for the nonstrict-feedback uncertain nonlinear high-order fully actuated (HOFA) systems with either uncertain constant delay or time-varying delay. Different from the previous works, the most difficult point is that the uncertain nonlinear function in the HOFA systems contains nonstrict feedback form and time delay in system states. In order to overcome this difficulty, the arbitrary approximation property of the radial basis function neural network (RBF NN) is used to estimate the unknown nonlinear functions. What’s more, the nonstrict-feedback form is transformed into strict-feedback strcture by using the property of Gaussian function. In addition, the appropriate Lyapunov-Krasovskii functions and separation techniques are used to compensate the effect of the unknown constant time delay or time-varying delay. Based on the HOFA system approaches, two adaptive NN controllers are proposed to ensure the system with constant time-delay and time-varying delay to be stabilized asymptotically, respectively. Finally, the proposed control strategies are applied to the thermoacoustic instability systems to demonstrate the feasibility and effectiveness of the obtained results.