Finite time stabilization for nonlinear systems with unstructured uncertainties

This paper investigates the finite time stabilization problem for a class of nonlinear systems with unknown control directions and unstructured uncertainties. The unstructured uncertainties indicate that not only the parameters but also the structure of the system nonlinearities are uncertain. In order to solve the above problem, a new adaptive controller is proposed. Logic-based switching rules are utilized to tune the controller parameters online to stabilize the system in finite time. Different from the existing logic-based adaptive controller for structured/parametric uncertainties, new switching barrier Lyapunov method and supervisory functions are introduced to overcome the obstacles caused by unstructured uncertainties and unknown control directions. Moreover, an extension is made for the proposed method such that all the system states can be regulated to zero in prescribed finite time. Simulations are conducted to verify the effectiveness of the proposed design scheme.

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