Continuous self-adaptive control using a smoothed variable structure controller

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Abstract
A new continuous self-adaptive scalar control law is developed from a straightforward modification of ‘sliding’ variable structure system theory. The controller needs no parameter identification and exhibits invariance to a class of parameter variations. The continuous controller identifies certain null spaces in the state space associated with the derivatives of the switching function defined for the variable structure system and adapts itself and the time-varying switching hyperplane accordingly. The justification of the scheme and the stability of the method are highlighted. Comparisons are drawn with a previously defined discontinuous self-adaptive controller based on variable structure system theory. The general results are illustrated through the simulation of second- and third-order systems.

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