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In this article, a preassigned finite time control problem of nonlinear systems in strict-feedback form is investigated. From the perspective of arbitrary settling time, an appropriate preassigned finite-time performance function (PFPF) is constructed, and the preassigned finite-time stability (PAFS) is established, where the settling (convergence) time is not only completely unconcerned with initial conditions and design parameters but also more flexible. Furthermore, the backstepping technique and reduced-order observer are used to obtain the preassigned finite-time control scheme. The stability criteria of PAFS are developed to guarantee that the output can quickly converge to an arbitrarily small zone in preassigned time, and all signals of the closed-loop control system are PAFS. In the end, simulation examples verify the effectiveness of the presented method.
Chen et al. (Thu,) studied this question.