Abstract
AbstractWe consider the control design for under‐actuated manipulator systems. The task is to drive the system to be close to a prescribed constraint. The system contains uncertainty. It is bounded where the bounding information is prescribed by a fuzzy set (e.g., the bound is close to 1). The initial condition is also prescribed by a fuzzy set. A class of robust control is proposed, which guarantees a deterministic performance. On top of that, the choice of a control design parameter is cast into a fuzzy‐theoretic setting. A performance index, consisting of accumulated fuzzy‐based system performance and control cost, is proposed. The optimal control design parameters, which minimize the performance index, can be obtained by solving two algebraic quartic (fourth‐order) equations. As a result, the control design problem, which addresses both fuzzy and optimal characteristics, is completely solved.
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