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In this article, a learning control design method for analyzing the convergence of nonlinear systems described by a class of differential-algebraic equations’ is developed. This method generalizes the previous methods for the study of the learning control problem of constrained mechanical systems to include a wider class of systems. Furthermore, the proposed design method allows us to analyze the role of force learning in the learning control of such a control system. We derive a sufficient condition for the convergence of both the motion and contact force of the systems as the operations are repeated. An application of the proposed controller to robotic manipulators with holonomic constraints is discussed, and simulation results of a constrained cylindrical robot are presented.

Learning control for a class of nonlinear differential-algebraic systems with application to constrained robots