This article concentrates upon the practical fixed-time adaptive neural tracking control problem of non-strict-feedback nonlinear systems with input delay and prescribed boundary constraints (PBCs). A modified appropriate auxiliary system is introduced to eliminate the complex calculations appeared in the input delay. The unknown nonlinear functions exist in non-strict-feedback nonlinear systems, which are approximated by the radial basis function neural networks. The adaptive practical fixed-time control strategy is developed based on a novel coordinate transformation by utilizing the backstepping algorithm. Under the proposed controller, it can be guaranteed that the tracking error satisfies the PBCs in fixed time and all the signals in the closed-loop system are bounded. Some numerical simulations verify the effectiveness of the control approach.

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The problem of event-triggered fixed-time control for state-constrained stochastic nonlinear systems is discussed in this article. Different from the Barrier Lyapunov Function (BLF)-based and Integral BLF-based schemes which rely on feasibility conditions (FCs), by introducing nonlinear state-dependent functions , the asymmetric time-varying state constraints are handled without FCs .Combining with the fixed-time stable theory and dynamic surface control technique with fixed-time filter, the fixed-time stability in probability of the closed-loop system is ensured and the problems of “explosion of complexity” and “singularity” are overcome. Furthermore, the novel fixed-time error compensation signals are designed to compensate filtering errors, and event-triggered control technique is used to save network resources. Simulations also illustrate the effectiveness of the proposed method.

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