Variable structure control using an adaptive boundary of system uncertainty

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Abstract
A class of dynamic system is discussed where its uncertainty can be described as a lumped model, called lumped uncertainty, and the lumped uncertainty is cone-bounded for the state variables. We first propose a simple adaptation law for the boundary of uncertainty. Then based on this adaptive boundary, variable structure control is presented to render uncertain dynamic systems asymptotically stable. When the parameter adaptation has been completed, the system trajectory is constrained by the prescribed switching surface of the sliding mode. We apply the proposed method to a variable length pendulum as an example in numerical simulations. Simulation has shown its effectiveness in the control of a class of uncertain dynamic systems.

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