Descriptor Recurrent Neural Network Model and ℒ2− Gain Control Design for Systems with Dry Friction

This paper presents a control design method for mechanical systems involving the Coulomb and Stribeck dry friction effects. The design method is based on a continuous-time recurrent neural network (RNN) descriptor model. The latter has the particularity of including a single nonlinearity verifying the well-known cone bounded condition. Hence, a nonlinear static feedback is proposed guaranteeing an efficient friction compensation and optimizing the ℒ
₂
- gain of the closed-loop. The design procedure is recast as an optimization problem under LMI constraints that can be solved efficiently. The relevance of the proposed approach is confirmed through a didactic example.