Chaos control via Mathieu-Van der Pol system and Linear Optimal Control design with a non-ideal excitation and parametric uncertainties
PublisherUniversitat Politècnica de Catalunya. CIMNE
Rights accessOpen Access
The hyper-chaotic Mathieu-Van der Pol system is an important autonomous system model, with four state variables and four Lyapunov exponents, three of which are positive. Also called the Tri-Chaos, the Mathieu-Van der Pol system was mathematically modeled via linear coupling of Mathieu and Van der Pol non-linear and non-autonomous systems. In this work, a non-ideal system based on the Mathieu-Van der Pol System is modeled considering its parameters as uncertain, which makes it closer to reality. Numerical simulations are presented demonstrating that the system has a chaotic behavior with three positive Lyapunov exponents. Given such unstable and unpredictable behavior, the linear optimal control design is proposed to reduce the chaotic movement of this system to a fixed point. The simulation results show that the identification by Linear Optimal Control is very effective.
CitationVicente, J. P. G.; Chavarette, F. R.; Roefero, L. G. P. Chaos control via Mathieu-Van der Pol system and Linear Optimal Control design with a non-ideal excitation and parametric uncertainties. "Revista internacional de métodos numéricos para cálculo y diseño en ingeniería", 2019, vol. 35, núm. 3.