Design of decentralized adaptive backstepping controllers with perturbation estimation for perturbed large-scale systems

Based on the Lyapunov stability theorem, a decentralized adaptive backstepping control with perturbation estimation scheme is proposed in this paper for a class of perturbed multi-input large-scale systems to solve regulation problems. The dynamic equations of the plant are firstly transformed into semi-strict feedback form, and then the decentralized controllers are designed by using backstepping control method to achieve the property of asymptotic stability. In addition, perturbation estimation mechanisms are employed so that there is no need to compute the derivatives of the virtual input functions, and the upper bounds of the perturbations as well as perturbation estimation errors are not required to be known in advance either. A numerical example is also given for demonstrating the feasibility of the proposed control scheme.