
doi: 10.3934/mbe.2023359
pmid: 37161195
<abstract><p>Finite-time stability (FTS) has attained great interest in nonlinear control systems in recent two decades. Fixed-time stability (FxTS) is an improved version of FTS in consideration of its settling time independent of the initial values. In this article, the adaptive fixed-time stabilization issue is studied for a kind of nonlinear systems with nonlinear parametric uncertainties and uncertain control coefficients. Using the adaptive estimate and the adding one power integrator (AOPI) design tool, we propose a two-phase control strategy, which makes that the system states tend to the origin in fixed-time, and other signals are bounded on $ [0, +\infty) $. We prove the main results by means of the recently developed fixed-time Lyapunov stability theory. Finally, we apply the proposed adaptive fixed-time stabilizing control strategy into the pendulum system, and the simulation results verify the efficacy of the presented method.</p></abstract>
parametric uncertainty, finite-time control, QA1-939, fixed-time stabilization, adaptive control, TP248.13-248.65, Mathematics, Biotechnology
parametric uncertainty, finite-time control, QA1-939, fixed-time stabilization, adaptive control, TP248.13-248.65, Mathematics, Biotechnology
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