In this paper sliding mode surface design is concerned with multi objective optimization for nonlinear continuous-time systems in the presence of matched and mismatched uncertainties and disturbances. In order to reduce the effect of uncertainties and disturbances on sliding motion, this problem is formulated as a well-motivated mixed H2/H∞ optimization problem and a constructive algorithm based on linear matrix inequality (LMI) is proposed. We also give an LMI-based sliding mode control law to direct the system trajectories onto the designed sliding surface. Finally, using a numerical example, we show the effectiveness of proposed method.

In this paper, a sliding mode controller with a generalized ℋ 2 performance is proposed for a unicycle-like mobile robot to implement the trajectory tracking mission. First, a kinematic controller is introduced for the mobile robot and generating the desired values of the linear and angular velocity for the dynamic controller. Secondly, a dynamic controller based on the sliding mode control with a generalized ℋ 2 performance is proposed to make the real velocity of the mobile robot and reach the desired velocity command. The stability properties of the controllers are proved by the Lyapunov method. This control law providing smaller errors and better performance to deal with the slipping of the wheels and parameter uncertainty. Simulation is carried out for a mobile robot to verify the performance of the proposed control scheme.

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