Passivity-Based Fractional-Order Sliding Mode Control for Fractional-Order Hyperchaotic Systems with Unknown Parameters

In this paper we investigate the problem of passivity-based sliding mode control for fractional-order hyperchaotic systems with unknown parameters. Utilizing the fractional calculus, the fractional-order sliding surface is chosen. The state trajectories of the closed-loop system reach the fractional-order sliding surface in finite time under the control of the designed controller. The control law ensures the asymptotical stability on the sliding surface. A parameter adjustment scheme for fractional-order integral sliding surface is proposed by using the linear matrix inequality approach. Finally, the simulation results demonstrate the effectiveness of the proposed method for the synchronization control of fractional-order hyperchaotic systems with unknown parameters.