Abstract
In this paper, we propose a novel Nussbaum-type design to cope with the problem in nonlinear dynamical systems with unknown control directions. First, a Nussbaum-based Lyapunov analysis for fixed-time stability is investigated to lay the theoretical foundation. On this basis, the Nussbaum-type adaptive backstepping control is designed with dynamic surface filters to avoid repeated differentiation. To further reduce the computational complexity, an event-triggered mechanism is combined with the Nussbaum-type gain design. With the above design schemes, the practical fixed-time stability of the overall feedback systems can be guaranteed with theoretical discussion. Finally, the feasibility of the presented design is validated by two simulation examples made in the end.
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