Abstract
In this chapter, the global adaptive finite-time stabilization is investigated by logic-based switching control for a class of uncertain nonlinear systems with the powers of positive odd rational numbers. Parametric uncertainties entering the state equations nonlinearly can be fast time-varying or jumping at unknown time instants, and the control coefficient appearing in the control channel can be unknown. The bounds of the parametric uncertainties and the unknown control coefficient are not required to know a priori. Our proposed controller is a switching-type one, in which a nonlinear controller with two parameters to be tuned is first designed by adding a power integrator, and then a switching mechanism is proposed to tune the parameters online to finite-time stabilize the system. An example is provided to demonstrate the effectiveness of the proposed result.
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Notes
- 1.
\(t_s \) memories the latest switching time, although at the beginning \(t_s \) is set equal to 0.
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Fu, J., Ma, R. (2021). Adaptive Finite-Time Stabilization of Uncertain Nonlinear Systems via Logic-Based Switchings. In: Stabilization and H∞ Control of Switched Dynamic Systems. Studies in Systems, Decision and Control, vol 310. Springer, Cham. https://doi.org/10.1007/978-3-030-54197-2_5
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DOI: https://doi.org/10.1007/978-3-030-54197-2_5
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