Neuroadaptive fault-tolerant control of state constrained pure-feedback systems: A collective backstepping design

In this work, we present a neuroadaptive and fault-tolerant tracking control scheme for uncertain nonlinear pure-feedback systems in the presence of time-varying and asymmetric full state constraints and unanticipated actuation failures. Instead of using multi-step recursive backstepping design, we employ a one-step approach for control development. By introducing a nonlinear coordinate transformation, we convert the original nonlinear system with asymmetrical state constraints into a new augmented one free from state constraints, which allows for the complete obviation of the feasibility conditions in the strategy. Furthermore, by making use of the feature from skew symmetric matrix in the augmented system, we develop the neural adaptive control algorithms collectively without the need for repetitive design procedure, in which only one Lyapunov function and one step derivation are involved, leading to a design approach whose synthesis complexity does not increase with the order of the system.