Chaos Suppression in Forced Chaotic Systems by Innovative Sliding Mode Control

The paper introduces a procedure for suppressing the chaos based on an innovative sliding mode control. The procedure forces the system trajectory to track a sliding surface by means of a continuous control law. At the same time, the control signal must be able to drive the system to reach, asymptotically, the prefixed equilibrium condition. To perform this task, a novel tracking control algorithm is exploited. The latter involves the solution of a multi-objective optimization problem with the dynamic constraint expressed by system differential equations. This optimization process is solved by an innovative computational procedure based on Lyapunov and Sensitivity theory. In order to validate the proposed method, this was applied to the Van der Pol chaotic oscillator. The simulation results demonstrated that the chaotic behavior is completely removed and the resulting system is not affected by the chattering problem.