Singularity-conquering tracking control of a class of chaotic systems using Zhang-gradient dynamics

This study investigates the tracking-control problems of the Lorenz, Chen and Lu chaotic systems. Note that the input-output linearisation method cannot solve these tracking-control problems because of the existence of singularities, at which such chaotic systems fail to have a well-defined relative degree. By combining Zhang dynamics and gradient dynamics, an effective controller-design method, termed Zhang-gradient (ZG) method, is proposed for tracking control of the three chaotic systems. This ZG method, with singularities conquered, is capable of solving the tracking-control problems of the chaotic systems. Both theoretical analyses and simulative verifications substantiate that the tracking controllers based on the ZG method can achieve satisfactory tracking accuracy and successfully conquer singularities encountered during the tracking-control process.