This paper considers a problem of designing an adaptive controller for a first order nonlinear system x'=-DTf(x)-bu, subject to bounded input and output disturbances. Unmodelled dynamics are also considered in the stability analysis and a dead zone in the parameters update law is used. The dead zone size does not depend neither on the disturbances nor on the magnitude of the unmodelled dynamics. In addition, the disturbances and parameter upperbounds are not assumed to be a priori known.
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In this article one of the greatest generalized methods for establishing the equilibrium equations of a rigid body and the set of rigid bodies is proposed. It is related to six equations of moments of force about six the edges of a reference tetragon. It is possible to obtain different alternatives by substituting the force moment-equation for the force project-equation. Four different forms of equilibrium are established. It is important writing equilibrium equations of bodies possible to apply the special software as Mathcad, Maple.
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