Anti-control of continuous-time dynamical systems

Based on two basic characteristics of continuous-time autonomous chaotic systems, namely being globally bounded while having a positive Lyapunov exponent, this paper develops a universal and practical anti-control approach to design a general continuous-time autonomous chaotic system via Lyapunov exponent placement. This self-unified approach is verified by mathematical analysis and validated by several typical systems designs with simulations. Compared to the common trial-and-error methods, this approach is semi-analytical with feasible guidelines for design and implementation. Finally, using the Shilnikov criteria, it is proved that the new approach yields a heteroclinic orbit in a three-dimensional autonomous system, therefore the resulting system is indeed chaotic in the sense of Shilnikov.

► This article develops a new method for designing general continuous-time autonomous chaotic systems. ► The new design method is universal, based on Lyapunov exponent placement. ► This self-unified method is semi-analytical with guidelines for design and implementation. ► This new method is mathematically rigorous. ► This new method guarantees the resulting system be chaotic in the sense of Shilnikov.