Free-will arbitrary time stabilisation problem for a class of nonlinear strict-feedback systems based on the backstepping method

In this paper, the problem of free-will arbitrary time stabilisation for a class of nonlinear systems is investigated. In an effort to extend the idea of fixed-time theory to a broader class of systems, a prescribed-time controller has been developed by the examination of a general form of the strict-feedback systems. By means of the designed control scheme, the arbitrary convergence of the system states is guaranteed. Furthermore, the implementation of this approach is independent of any initial values and system design parameters. In real-world applications, this approach can be used to achieve system stability in terms of efficient time management. For many well-known systems, the proposed control can be used to solve the pre-defined convergence problem of asymptotic and finite-time controllers. Based on the backstepping control strategy, the stability of the proposed method for a strict-feedback system is demonstrated in the design section. Ultimately, the simulation results verify the accuracy and effectiveness of the proposed method.