Then, an adaptive compensation controller is constructed by utilizing the backstepping technique.
A distributed adaptive control scheme is constructed by combining Lyapunov Krasovskii functionals, backstepping methods, neural networks (NNs), auxiliary systems, graph theory, the mean value theorem and the implicit function theory along with the dynamic surface control (DSC) technique.
Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov Krasovskii functionals and the backstepping approach.
Neural networks are utilized to approximate unknown nonlinear functions, and an adaptive decentralized controller is constructed by incorporating the minimal learning parameters algorithm into backstepping design procedure.
The external disturbance and the system uncertainty are efficiently tackled using a Nussbaum disturbance observer (NDO), and the adaptive controller is constructed by combining the dynamic surface control technique to handle the problem of "explosion of complexity" inherent in the conventional backstepping method.
Two classes of state feedback controllers are constructed by adopting the adaptive backstepping technique, and both of them are designed by using the common Lyapunov function (CLF) method.
Decentralized robust controllers are constructed by a Lyapunov-based recursive design technique, backstepping with the aid of augmentation, so that the corresponding closed-loop system is globally asymptotically stable for all possible uncertain parameters and interconnections.
Under the assumption that all the growth conditions for the unknown nonlinear perturbation functions are partially known, the common finite-time controller and adaptive law are constructed by extending the adding-a-power-integrator technique and using the backstepping methodology.
