U-Model Based Adaptive Neural Networks Fixed-Time Backstepping Control for Uncertain Nonlinear System

Under U-model control design framework, a fixed-time neural networks adaptive backstepping control is proposed. The majority of the previously described adaptive neural controllers were based on uniformly ultimately bounded (UUB) or practical finite stable (PFS) theory. For neural networks control, it makes the control law as well as stability analysis highly lengthy and complicated because of the unknown ideal weight and unknown approximation error. Moreover, there has been very limited research focus on adaptive law for neural networks adaptive control in finite time. Based on fixed-time stability theory, a fixed-time bounded theory is proposed for fixed-time neural networks adaptive backstepping control. The most outstanding novelty is that fixed-time adaptive law for training weights of neural networks is proposed for fixed-time neural networks adaptive control. Furthermore, by combining fixed-time adaptive law and Lyapunov-based arguments, a valid fixed-time controller design algorithm is presented with universal approximation property of neural networks to ensure the system is fixed-time bounded, rather than PFS or UUB. The controller guarantees closed-loop system fixed-time bounded in the Lyapunov sense. The benchmark simulation demonstrated effectiveness and efficiency of the proposed approach.