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Uncertain Polytopic LPV Modelling of Robot Manipulators and Trajectory Tracking

Mohammad Bagher Abolhasani Jabali and Mohammad Hosein Kazemi*
International Journal of Control, Automation, and Systems, vol. 15, no. 2, pp.883-891, 2017

Abstract : "This research work proposes a full state systematic feedback control design method for some classes of non-linear systems which are forced to follow a specific desired trajectory, such as robotic systems, using uncertain polytopic linear parameter-varying (LPV) modelling approach. An LPV representation of the system is generated from linearization of its usual Lagrangian equation about a desired state trajectory and is reduced to an uncertain polytopic one. A vector of scheduling signals from the desired trajectory information is produced to construct the LPV model. The control gain matrix is derived by solving a set of linear matrix inequalities (LMIs) that returns the sufficiently small value of the time derivative of the Lyapunov function. A sufficient condition is proposed to guarantee the asymptotic stability of the closed-loop LPV systems against the uncertainties on the vertices. The proposed scheme is applied to controller synthesis of a two-degree-of-freedom robotic manipulator trajectory tracking problem."

Keyword : LMI, LPV system, nonlinear systems, polytopic representation, robot manipulator, robust design.

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