Sliding mode optimization in robot dynamics with LPV controller design

This letter extends previous results on constrained optimization control problems of uncertain robot systems based on sliding modes generation. An equivalent linear parameter varying (LPV) state-space representation of the nonlinear robot model is considered to design a stabilizing state-feedback control law by solving linear matrix inequalities (LMI) with structural constraints. The finite-time regulation of the state trajectory to a desired reference, while minimizing a pre-specified cost function with state constraints, is then solved by a sliding mode approach relying on the considered parameter-dependent structure of the robot system. Stability conditions of the proposed approach are provided, and a realistic numerical example verifies the effectiveness of the proposed technique.