Dynamic Analysis and Synchronization for a System with Hyperchaotic Behavior

In this work, dynamical analysis and synchronization control for a four-dimensional Lorenz system are presented. Numerical simulations have shown that for certain parameters, the system has chaotic or recurrent behavior. The chaotic behavior is analyzed by means of phase portraits, bifurcation diagram, fast Fourier transform, and Lyapunov exponents calculation. The synchronization control strategy involves the application of two control signals: a nonlinear feedforward control to maintain the synchronization and a state feedback control to synchronize with the system. Two control strategies are presented for the feedback control project, one considering the State-Dependent Riccati Equation (SDRE) accounting for a nonlinear state matrix and a second one accounting for the Optimal Linear Feedback Control (OLFC), whose state matrix is linear. In addition, the control robustness is investigated through analyzing parametric errors.