Non-Singular Fixed-Time Tracking Control of Uncertain Nonlinear Pure-Feedback Systems With Practical State Constraints

In this paper, a fixed-time tracking control problem is investigated for an uncertain high-order nonlinear pure-feedback systems with practical state constraints. To this end, a new nonlinear transformation function with lower change rate at the state constraint boundary is first proposed, which can not only handle both constrained and unconstrained states in a unified way, but also reduce the control magnitude at the constraint boundary. With the help of the proposed transformation function, the original system is transformed to a new system without state constraints. Then, a non-singular fixed-time adaptive tracking controller is designed by applying an adding a power integrator technique and an adaptive neural network method. It is shown that the practical fixed-time stability can be guaranteed for the closed-loop system under the proposed tracking controller. Finally, two numerical examples are presented to demonstrate the proposed fixed-time tracking control strategy.